Question

Simplify the following?

(2x/(x² - 9)-(5/(x² 4x + 3))

Answer 1

The expression is [2x/(x² - 9)] - [5/(x² + 4x + 3)]

First simplify the denominators.

x² - 9 = x² - 3²

{Apply the formula a² - b² = (a - b)(a + b), a = x, b = 3}

= ( x - 3)(x + 3)

Now factorize x² + 4x + 3

= x² + 3x + x + 3

= x(x + 3) + 1(x + 3)

= (x + 3)(x + 1)

Now the expression is 2x/[(x - 3)(x + 3)] - 5/[(x + 3)(x + 1)]

= [2x(x + 1) - 5(x - 3)]/[(x - 3)(x + 3)(x + 1)]

= (2x² + 2x - 5x + 15)/(x² - 9)(x + 1)

= (2x² - 3x + 15)/(x² - 9)(x + 1)

[2x/(x² - 9)] - [5/(x² + 4x + 3)] = (2x² - 3x + 15)/(x² - 9)(x + 1).