Question

Solve the equation and verify your answer:

(x+2)/(x+5) = x/(x+6)

Answer 1

We have,

(x+2)/(x+5) = x/(x+6)

(x+2)/(x+5) – x/(x+6) = 0

By taking LCM as (x+5) (x+6)

((x+2) (x+6) – x(x+5)) / (x+5) (x+6) = 0

By cross-multiplying we get,

(x+2) (x+6) – x(x+5) = 0

Upon expansion,

x² + 8x + 12 – x² – 5x = 0

3x + 12 = 0

3x = -12

x = -12/3

= -4

Now let us verify the given equation,

(x+2)/(x+5) = x/(x+6)

By substituting the value of ‘x’ we get,

(-4 + 2) / (-4 + 5) = -4 / (-4 + 6)

-2/1 = -4 / (2)

-2 = -2

Hence, the given equation is verified.