63.0k views
0 votes
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

1 Answer

4 votes

Answer:

(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)

User Toinbis
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories