Question

Solve the following quadratic equations by factorization:

`(x + 3)/(x + 2) = (3x - 7)/(2x - 3); x ≠ -2, 3/2`

Answer 1

We have been given

`(x+3)/(x+2)=(3x-7)/(2x-3)`

2x² - 3x + 6x - 9 = 3x² - 7x + 6x - 14

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x + 1)(x - 5) = 0

Therefore,

x + 1 = 0

x = -1

or,

x - 5 = 0

x = 5

Hence, x = -1 or x = 5.