Question

2- x+1/x-2 - x-4/x+2 can be written as a single fraction in the form ax+b/x^2 - 4, where a and b are integers. work out the value of a and the value of b

Answer 1

(3x - 8)/(x^2 -4)

Explanation:

We want to convert:

2- x+1/x-2 - x-4/x+2

2- (x+1)/(x-2) - (x-4)/(x+2) [Parentheses added]

to a fraction with a form of

(ax+b)/(x^2 - 4) [Parentheses added]

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

Multiply the first term by (x+2)/(x+2) and the second by (x-2)/(x-2).

2- [(x+1)/(x-2)]*(x+2)/(x+2) - [(x-4)/(x+2)]*(x-2)/(x-2)

2- [(x+1)(x+2)/(x-2)(x+2)] - [(x-4)(x-2)/(x+2)(x-2)]

2 - (x+1)(x+2)/(x^2 -4) - (x-4)(x-2)/(x^2 -4)

2 - [(x+1)(x+2) - (x-4)(x-2)]/(x^2 -4)

2 - [(x^2 + 3x + 2) - (x^2 - 6x +8)]/(x^2 -4)

2 - [(x^2 + 3x + 2 - x^2 - 6x +8)]/(x^2 -4)

2 - [- 3x + 10)/(x^2 -4)

2 + 3x - 10)/(x^2 -4)

(3x - 8)/(x^2 -4)