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# Maths help-equations watch

1. What is the answer to this? Can you show working please?!
1/x-2 + 3/x+6 =1/2
2. (Original post by isabel12144)
1/x-2 + 3/x+6 =1/2
You should remove ambiguity by using brackets, so it would be, I'm assuming 1/(x-2) + 3(x+6) = 1/2, right, that is:

.

Multiply throughout by and then expand brackets and solve the remaining quadratic:

- multiply both sides by two, re-arrange, etc... and then solve the quadratic.
3. (Original post by isabel12144)
1/x-2 + 3/x+6 =1/2
What do you think you should do? (hint: you've got some fractions there ...)
4. (Original post by SeanFM)
What do you think you should do? (hint: you've got some fractions there ...)
I did this:
x+6/(x-2)(x+6) + 3(x-2)/(x-2)(x+6)

x+6+3x-6/(x-2)(x+6) = 4x/(x-2)(x+6)

4x/(x-2)(x+6)=1/2

Then I didn't know what to do.
5. (Original post by isabel12144)
I did this:
x+6/(x-2)(x+6) + 3(x-2)/(x-2)(x+6)

x+6+3x-6/(x-2)(x+6) = 4x/(x-2)(x+6)

4x/(x-2)(x+6)=1/2

Then I didn't know what to do.
Good work

Now it may help to 'get rid' of the fractions on each side so you can form a quadratic equation.. any ideas?
6. (Original post by SeanFM)
Good work

Now it may help to 'get rid' of the fractions on each side so you can form a quadratic equation.. any ideas?
Do you do?

4x=1/2*(x-2)(x-6)
7. (Original post by isabel12144)
Do you do?

4x=1/2*(x-2)(x-6)
Careful with how you write things but yes, as long as that's that's fine, and you can also 'get rid' of the 1/2 on the right hand side...

What next?
8. (Original post by SeanFM)
Careful with how you write things but yes, as long as that's that's fine, and you can also 'get rid' of the 1/2 on the right hand side...

What next?
8x=(x-2)(x+6)
?
9. (Original post by isabel12144)
8x=(x-2)(x+6)
?
Correct now what can you do?
10. (Original post by isabel12144)
8x=(x-2)(x+6)
?
Keep going...

Hint (only if you need it)
Spoiler:
Show
You can expand the brackets
11. (Original post by SeanFM)
Correct now what can you do?
8x=x^2+4x-12
12. (Original post by isabel12144)
8x=x^2+4x-12
Yep, so it almost looks like a quadratic that you can solve. What's next?
13. (Original post by SeanFM)
Yep, so it almost looks like a quadratic that you can solve. What's next?
8x+12=x^2+4x
12=x^2-4x
14. (Original post by isabel12144)
8x+12=x^2+4x
12=x^2-4x
If you rearrange the equation so it equals 0, it might be easier to solve
15. (Original post by Andy98)
If you rearrange the equation so it equals 0, it might be easier to solve
is it this then?
x^2-4x-12=0
(x-6)(x+2)=0
x=-6 or 2
16. (Original post by isabel12144)
is it this then?
x^2-4x-12=0
(x-6)(x+2)=0
x=-6 or 2
You got the factorisation right, but the solutions incorrect
17. (Original post by isabel12144)
is it this then?
x^2-4x-12=0
(x-6)(x+2)=0
x=-6 or 2
Almost - remember, you have to work out:
x-6=0 and x+2=0
18. (Original post by isabel12144)
is it this then?
x^2-4x-12=0
(x-6)(x+2)=0
x=-6 or 2
for (x-6)(x+2)=0
either x-6=0 or x+2=0
if you rearrange these you should get the correct values for x
19. (Original post by Andy98)
You got the factorisation right, but the solutions incorrect
x=-2 or 6
20. (Original post by isabel12144)
x=-2 or 6
correct.

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