Question

Write in lowest terms: $\frac{2x^2 - 3x - 2}{2x^2 - 5x - 3}$

Answer 1

on factorising $2 x^{2} -3x-2$ we get $(x-2)(2x+1)$
on factorising $2 x^{2} -5x-3$ we get $(x-3)(2x+1)$
$(2x+1)$ will be cancelled and we get $\frac{x-2}{x-3}$

Answer 2

When we solve, 2x^2-3x-2 = (2x+1)(x-2)
When we solve, 2x^2-5x-3 = (2x+1)(x-3)

Therefore, (2x+1)(x-2)/(2x+1)(x-3) = (x-2)(x-3).