Question

2- (x+3)/x-4 - (x-7)/x+4 can be written as a single fraction in the form (ax+b)/x²-16

where a and b are integers. Work out the value of a and the value of b.

Answer 1

To combine the given expression into a single fraction, find a common denominator for the two fractions and simplify the expression. The value of a is -2 and the value of b is 12.

Step-by-step explanation:

To combine the given expression into a single fraction, we need to find a common denominator for the two fractions.

The common denominator will be the product of the denominators, which in this case is (x-4)(x+4).

We then multiply each fraction by its missing factor to get a common denominator:

(2-(x+3)/(x-4)) * (x+4)/(x+4) - (x-7)/(x+4) * (x-4)/(x-4)

Simplifying further, we get (2x+8-x-3-x+7)/(x^2-16).

Combining like terms, the numerator becomes (-2x+12)/(x^2-16).

Therefore, the value of a is -2 and the value of b is 12.