Simplify a 2xx2 1 xx 1 b 5x 12x2 3x x 2x 3Solutiona

Simplify: a) 2x/x^2 - 1 - x/x + 1 b) 5x = 12/x^2 + 3x + x + 2/x = 3

Solution

a)

2x/(x² - 1) - x/(x + 1)

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

Now taking LCM = (x + 1)(x - 1), we have

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

= (2x - x² + x)/(x + 1)(x - 1)

= (3x - x²)/(x² - 1)

= x(3 - x)/(x² - 1) ANS

b)

(5x + 12)/(x² + 3x) + (x + 2)/(x + 3)

= (5x + 12)/x(x + 3) + (x + 2)/(x + 3)

Taking LCM = x(x + 3), we have

= (5x + 12 + x² + 2x)/x(x + 3)

= (x² + 7x + 12)/x(x + 3)

Now making the numerator a perfect square, we have

= [(x + 7/2)² - (1/2)²] / x(x + 3)

= [(x + 7/2 +1/2)(x + 7/2 - 1/2)] / x(x + 3)

= (x + 4)(x + 3) / x (x + 3)

= (x + 4) / x ANS