Question

Please, someone. Solve for x.

Answer 1

Combine the fractions on the left side:

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

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

(9x - 18) / ((x + 2) (x - 2)) + (2x + 4) / ((x + 2) (x - 2)) = 1

(9x - 18 + 2x + 4) / ((x + 2) (x - 2)) = 1

(11x - 14) / ((x + 2) (x - 2)) = 1

Recall the difference of squares identity,

a² - b² = (a + b) (a - b)

which lets us simplify the denominator on the left side as

(11x - 14) / (x² - 4) = 1

For any real numbers a and b, if a/b = 1, then a = b. This means

11x - 14 = x² - 4

which we can rearrange as

x² - 11x + 10 = 0

Factorize the left side:

(x - 10) (x - 1) = 0

Then

x - 10 = 0   or   x - 1 = 0

x = 10   or   x = 1