Question

Using properties of proportion, find the value of ‘x’:

`(6x^2 + 3x − 5)/(3x − 5) = (9x^2 + 2x + 5)/(2x + 5); x ≠ 0`

Answer 1

Given:

`(6x^2 + 3x − 5)/(3x − 5) = (9x^2 + 2x + 5)/(2x + 5); x ≠ 0`

`(6x^2 + 3x − 5 + 3x − 5)/(6x^2 + 3x − 5 − 3x + 5) = (9x^2 + 2x + 5 + 2x + 5)/(9x^2 + 2x + 5 − 2x − 5)`

Simplifying both sides:

`(6x^2 + 6x − 10​)/(6x^2) = (9x^2 + 4x + 10)/(9x^2)`

Reducing further:

`(6x^2 + 6x − 10)/2 = (9x^2 + 4x + 10)/3`

Cross-multiplying:

18x² + 18x − 30 = 18x² + 8x + 20

10x = 50

x = 5