Can anyone solve this?

So I am going to be doing higher IB maths next year, and my maths teacher set me some mymaths tasks to do. Mymaths is an online maths homework website. The only problem is, I have never been taught this before and mymaths' explanations seem to be... lacking.
One exercise I had to do was solving algebraic equations with fractions.
I managed to get all the questions correct except this type of question, and I was wondering if anyone could solve it?

If anyone can, could you please explain how you did it, because I am stumped.
Thank you :smile:

Edit:When I said solve it, I wanted to know if anyone could find the two possible values of x.

EDIT:
Here is my working

(4/x-6)- (3/x-1)=-4

4-(3(x-6)/x-1)=-4(x-6)

(4x-4)-(3x-18)=-4x^2+28x-24

x=22=-4x^2+28x-24

x=-4x^2+28x-2

0=-4x^2+27x-2

Using the quadratic formula, the two answers that I got were
x=-3.45
x=23.55

Is this correct?

(edited 10 years ago)

Reply 1

Extricated

17

Do you know how to subtract fractions? Make the denominators the same by multiplying through...it is quite simple from there..

Reply 2

samiito

OP

Original post by Extricated

Do you know how to subtract fractions? Make the denominators the same by multiplying through...it is quite simple from there..

I probably should have been clearer. I meant can anybody find the two possible values of x.

Reply 3

physics4ever

11

have you tried multipying both sides by (x-6)(x-1)

Reply 4

Bloxorus

16

Cross multiply the fractions so you get 4(x-1) - 3(x-6) = -4(x-6)(x-1)

Then expand the brackets: (4x-4) - (3x-18) = -4x^2+28x-24

Simplify: x+14 = -4x^2+28x-24 ---> -4x^2+27x-38 =0

Then just complete the square/use quadratic formula from there.

Hope that helps :smile:

(edited 10 years ago)

Reply 5

samiito

OP

Original post by physics4ever

have you tried multipying both sides by (x-6)(x-1)

Yes I have.
I then simplified the question until it read like a quadratic equation, such as
0=-4x^2+28x-24.
Then I factorised this quadratic and used the quadratic formula to find the two possible values of x.
However these two values were not correct.

Reply 6

BadAtMaths1

Original post by Bloxorus

Cross multiply the fractions so you get 4(x-1) - 3(x-6) = -4

Then expand the brackets: (4x-4) - (3x-18) = -4

Simplify: x+14 = -4 ---> x=-18

Hope that helps :smile:

This is wrong OP. The right hand side of the equation should read -4(x-1)(x-6).

Reply 7

samiito

OP

Original post by BadAtMaths1

This is wrong OP. The right hand side of the equation should read -4(x-1)(x-6).

That it what I got, dumb question, but what would you then do?
would you multiply (x-1)(x-6) together and then multiply it all by -4?
Or would you multiply (x-1) by -4 and then multiply (-4x+4) by (x-6)?

Reply 8

BabyMaths

Original post by samiito

Yes I have.
I then simplified the question until it read like a quadratic equation, such as
0=-4x^2+28x-24.
Then I factorised this quadratic and used the quadratic formula to find the two possible values of x.
However these two values were not correct.

To avoid wasting everyone's time you should have said how far you have got and post working.

You appear to know how to solve it so you probably just made a small slip that someone will easily spot if...

Reply 9

BabyMaths

Original post by samiito

That it what I got, dumb question, but what would you then do?
would you multiply (x-1)(x-6) together and then multiply it all by -4?
Or would you multiply (x-1) by -4 and then multiply (-4x+4) by (x-6)?

Either way is fine.

Reply 10

physics4ever

11

Original post by samiito

Yes I have.
I then simplified the question until it read like a quadratic equation, such as
0=-4x^2+27x-24.
Then I factorised this quadratic and used the quadratic formula to find the two possible values of x.
However these two values were not correct.

it should be 0=-4x^2+28x-38,check that you multiplied out the brackets with correct signs,minus x minus is +
my answers were 2 and 4.75

EDIT: you should have got 4(x-1)-3(x-6)=-4(x-6)(x-1) and expanded

(edited 10 years ago)

Reply 11

Bloxorus

16

Original post by BadAtMaths1

This is wrong OP. The right hand side of the equation should read -4(x-1)(x-6).

Just noticed that, thanks.

Reply 12

gdunne42

21

Original post by samiito

Yes I have.
I then simplified the question until it read like a quadratic equation, such as
0=-4x^2+28x-24.
Then I factorised this quadratic and used the quadratic formula to find the two possible values of x.
However these two values were not correct.

there's your mistake

that quadratic does not = 0

Reply 13

fat_hampster

1

Original post by samiito

That it what I got, dumb question, but what would you then do?
would you multiply (x-1)(x-6) together and then multiply it all by -4?
Or would you multiply (x-1) by -4 and then multiply (-4x+4) by (x-6)?

Try them both, you should find that the order you multiply doesn't make any difference.

Original post by samiito

Yes I have.
I then simplified the question until it read like a quadratic equation, such as
0=-4x^2+28x-24.
Then I factorised this quadratic and used the quadratic formula to find the two possible values of x.
However these two values were not correct.

You're right hand side is -4(x-1)(x-6), but you've missed what was originally on the left hand side.

What you've done is like saying 12/x = 3 so 0 = 3 * x.

(4/(x-6))*(x-1)(x-6) = 4(x-1). You should be able to work out the rest from there.

Reply 14

Bloxorus

16

Original post by samiito

That it what I got, dumb question, but what would you then do?
would you multiply (x-1)(x-6) together and then multiply it all by -4?
Or would you multiply (x-1) by -4 and then multiply (-4x+4) by (x-6)?

I just updated my post above, I think its correct now.

Reply 15

BabyMaths

Original post by physics4ever

it should be 0=-4x^2+28x-38,check that you multiplied out the brackets with correct signs,minus x minus is +
my answers were 2 and 4.75

Almost. Answers correct though.

Reply 16

samiito

OP

Original post by BabyMaths

To avoid wasting everyone's time you should have said how far you have got and post working.

You appear to know how to solve it so you probably just made a small slip that someone will easily spot if...

I've edited the OP

Reply 17

samiito

OP

Original post by BabyMaths

Either way is fine.

Original post by physics4ever

it should be 0=-4x^2+28x-38,check that you multiplied out the brackets with correct signs,minus x minus is +
my answers were 2 and 4.75

EDIT: you should have got 4(x-1)-3(x-6)=-4(x-6)(x-1) and expanded

Original post by gdunne42

there's your mistake

that quadratic does not = 0

Original post by fat_hampster

Try them both, you should find that the order you multiply doesn't make any difference.

You're right hand side is -4(x-1)(x-6), but you've missed what was originally on the left hand side.

What you've done is like saying 12/x = 3 so 0 = 3 * x.

(4/(x-6))*(x-1)(x-6) = 4(x-1). You should be able to work out the rest from there.