Question

Find the values for x for which the expression 2x-3/(x+4)(x-2) is equal to 1/5​

Answer 1

`((2x - 3))/((x + 4)(x - 2)) = (1)/(5) \\ \frac{2x - 3}{x {}^(2) - 2x + 4x - 8} = (1)/(5) \\ x {}^(2) - 2x + 4x - 8 = 5(2x - 3) \\ x {}^(2) + 2x - 8 = 10x - 15 \\ x {}^(2) + 2x - 10x = - 15 + 8 \\ x { }^(2) - 8x = - 7 \\ x {}^(2) - 8x + 7 = 0 \\ x {}^(2) - x - 7x + 7 = 0 \\ x(x - 1) + 7(x - 1) \\ x + 7 = 0 \\ x = - 7or \\ x - 1 = 0 \\ x = 1`

Explanation:

x=7 or x=1

Answer 2

1 and 7

Explanation:

(x+4)(x-2) = x²+2x-8

set up proportion:

2x-3/ x²+2x-8 = 1/5

cross-multiply:

5(2x-3) = x²+2x-8

10x-15 = x²+2x-8

Combine Like Terms:

x²-8x+7

Factor:

(x-7)(x-1)

set each factor equal to zero and solve: x = 1, x = 7