[Qu33n]

Hey, I did a past paper yesterday and i got this question:

Simplify fully x(sqrd) -8x +15 / 2x(sqrd) - 7x - 15

I don't get it will someone please give me an answer to this and some explanation PLEASE?

[RajPopat94]

(Original post by Qu33n)
Hey, I did a past paper yesterday and i got this question:

Simplify fully x(sqrd) -8x +15 / 2x(sqrd) - 7x - 15

I don't get it will someone please give me an answer to this and some explanation PLEASE?

If you factorise both the numerator and denominator, what do you get?

In these questions, the likelihood is that when you factorise, one of the brackets in the numerator will cancel with one of the brackets in the denominator

[dugdugdug]

(Original post by Qu33n)
Hey, I did a past paper yesterday and i got this question:

Simplify fully x(sqrd) -8x +15 / 2x(sqrd) - 7x - 15

I don't get it will someone please give me an answer to this and some explanation PLEASE?

x^2-8x+15 factorises to (x-3)(x-5)

2x^2-7x-15 factorises to (2x+3)(x-5)

because

2x^2-7x-15

= 2x^2-10x+3x-15

= 2x(x-5)+3(x-5)

= (2x+3)(x-5)

So answer is (x-3)/(2x+3)

[Qu33n]

(Original post by dugdugdug)
x^2-8x+15 factorises to (x-3)(x-5)

2x^2-7x-15 factorises to (2x+3)(x-5)

because

2x^2-7x-15

= 2x^2-10x+3x-15

= 2x(x-5)+3(x-5)

= (2x+3)(x-5)

So answer is (x-3)/(2x+3)

Right! Now, you may think I'm daft, but, I still don't understand how you got the bottom line lool! I got the top line the same as you, but the bottom one has to add up to -7 not -8 so I'm confused how you used the same numbers, 3 and 5.

Thanks for helping btw

[Qu33n]

(Original post by RajPopat94)
If you factorise both the numerator and denominator, what do you get?

In these questions, the likelihood is that when you factorise, one of the brackets in the numerator will cancel with one of the brackets in the denominator

Yeah I get that but I don't get which numbers go for the bottom two brackets :/

[TGH1]

(Original post by Qu33n)
the bottom one has to add up to -7 not -8

-10x + 3x = -7x

[Qu33n]

(Original post by TGH1)
-10x + 3x = -7x

But doesn't it have to times together to make 15 too loool am confused

[dugdugdug]

(Original post by Qu33n)
But doesn't it have to times together to make 15 too loool am confused

Here's some general theory behind factorising.

Given an equation ax^2+bx+c = 0

Case 1: a = 1

You need to find the factors of c that add up to b.

In the example x^2-8x+15, you need to find the factors of 15 that add up to -8. These factors are -3 and -5.

Hence (x-3)(x-5) = 0

Case 2: a>1

You need to find the factors of ac that add up to b.

In the example 2x^2-7x-15, you need to find the factors of 2 times -15, ie -30 that add up to -7. These factors are -10 and 3.

Now rewrite original expression with the middle term (the x term) split up.

It was -7x but rewrite it as -10x+3x

So 2x^2-7x-15

= 2x^2-10x+3x-15

Consider 2x^2-10x which factorises to 2x(x-5)

Consider 3x-15 which factorises to 3(x-5)

Both have a common (x-5)

so 2x^2-10x+3x-15 becomes 2x(x-5)+3(x-5)

= (2x+3)(x-5) by the DISTRIBUTIVE LAW

[Qu33n]

(Original post by dugdugdug)
Here's some general theory behind factorising.

Given an equation ax^2+bx+c = 0

Case 1: a = 1

You need to find the factors of c that add up to b.

In the example x^2-8x+15, you need to find the factors of 15 that add up to -8. These factors are -3 and -5.

Hence (x-3)(x-5) = 0

Case 2: a>1

You need to find the factors of ac that add up to b.

In the example 2x^2-7x-15, you need to find the factors of 2 times -15, ie -30 that add up to -7. These factors are -10 and 3.

Now rewrite original expression with the middle term (the x term) split up.

It was -7x but rewrite it as -10x+3x

So 2x^2-7x-15

= 2x^2-10x+3x-15

Consider 2x^2-10x which factorises to 2x(x-5)

Consider 3x-15 which factorises to 3(x-5)

Both have a common (x-5)

so 2x^2-10x+3x-15 becomes 2x(x-5)+3(x-5)

= (2x+3)(x-5) by the DISTRIBUTIVE LAW

Ahh!! Thanks I think I finally get it