Question

Solve for x :
(x + 3)/(x – 1) = (2x + 1)/(3x – 5)

Answer 1

The solution for x in (x + 3) / (x – 1) = (2x + 1) / (3x – 5) is x = -7, and x = 2.

• (x + 3) / (x – 1) = (2x + 1) / (3x – 5)

Applying cross-multiplication, we get,

( x + 3 ) (3x - 5 ) = (2x + 1) ( x - 1)

Or, (x × 3x) + (x × -5) + (3 × 3x) + (3 × -5) = (2x × x) + (2x × -1) + (1 × x) + (1 × -1)

Or, 3x² - 5x + 9x - 15 = 2x² - 2x + x - 1

Or, 3x² + 4x - 15 = 2x² - x - 1

Or, 3x² - 2x² + 4x + x - 15 + 1 = 0

Or, x² + 5x - 14 = 0

• Now, we have to solve the quadratic equation x² + 5x - 14 = 0

x² + 5x - 14 = 0

Or, x² + 7x - 2x - 14 = 0

Or, x (x + 7) - 2 (x + 7) = 0

Or, (x + 7) (x - 2) = 0

Or, x + 7 = 0 ; x - 2 = 0

Or, x = -7 ; x = 2

Therefore, the values of x are -7 and 2.

Answer 2

Values of x are -7 and +2.

Explanation:

(x + 3)/(x – 1) = (2x + 1)/(3x – 5)

(x+3) (3x-5) = (2x+1) (x-1)

3x^2 +9x - 5x - 15 = 2x^2 + x - 2x - 1

3x^2 + 4x - 15 = 2x^2 - x - 1

x^2 + 5x - 14 = 0

To solve, we can write the equation as:

x^2 + 5x - 14  = x^2 + 7x - 2x - 14

x (x + 7) - 2 (x+7) = 0

(x + 7) (x - 2) = 0

So the factors of the given expression are (x+7) and (x-2).

Values of x are -7 and +2.