Maths question. Please help?

Question

Could someone please help me with this question, and tell me how to do it. Exam today at 2 O'clock !!!!!!!!

http://www.gcsemathspastpapers.com/images/p5j01q52.gif

Answer 1

3 / (x - 5) + 1 / ( x + 1 ) = (3(x + 1) + 1( x - 5) ) / (x - 5)( x + 1 )
= (3x + 3 + x - 5 ) / (x - 5)( x + 1 )
= (4x - 2 ) / (x - 5)( x + 1 )

3 / (x - 5) + 1 / ( x + 1 ) = 2/5
:> (4x - 2 ) / (x - 5)( x + 1 ) = 2/5 (cross multiplication)
:. 5(4x - 2 ) = 2(x - 5)( x + 1 )
20x - 10 = 2(x^2 - 4x - 5)
20x - 10 = 2x^2 - 8x -10
2x^2 - 8x - 20x -10 = 0
2x^2 - 28x = 0
x^2 - 14x= 0
x(x - 14 ) = 0
either x = 0 or x = 14

Answer 2

Multiply both sides by product of the denominators:
3(x+1) + 1(x-5) = 4x -2

Multiply by 5
15/x-5 + 5/x+1 = 2
Divide by 2
15 /2x-10 + 5/2x+2
Multiply by product of denominators
30x +30 + 10x -50=0
40x=20
x = 1/2

Answer 3

3/(x-5) + 1/(x+1) = (3x+3+x-5)/(x-5)(x+1) =
(4x-2)/(x-5)(x+1) =>
(4x-2) / (x-5)(x+1) = 2/5
=>20x-10 = 2(x^2 -4x -5)
=>20x -10 = 2x^2 - 8x -10
=> x^2 - 14x = 0
=> x(x-14) = 0
=> X = 0 , X =14

Answer 4

the right answer is x=0 and x = 14

Answer 5

i -
= 3(x+1) +( x-5)
_______________
(x-5)(x+1)

= 3x+3+x-5
________
(x-5)(x+1)

= 4x - 2
_____
x^2 -10x - 5



ii -


20x-10 =2x^2 -20x -10
2x^2-40x =0
x^2 - 20 = 0

x ( x-20) = 0

x = 0 or x = 20