Question

For what value of x will 2x + 1/3x -2 and 3x - 4 / x + 8 represent the same fraction ? Also find the fraction

Answer 1

Given that the two fractions are the same:

$\dfrac{2x + 1}{3x - 2} = \dfrac{3x- 4}{x + 8}$

Cross multiply:

$(2x + 1) (x + 8) = (3x - 4) (3x - 2)$

Expand:

$2x^2 + 16x + x + 8 = 9x^2 - 6x - 12x + 8$

Combine like terms:

$2x^2 + 17x + 8 = 9x^2 - 18x + 8$

Move all to the LHS:

$2x^2 + 17x + 8 - 9x^2 + 18x - 8 = 0$

Combine like terms:

$-7x^2 + 35x = 0$

Multiply -1 through:

$7x^2 - 35x = 0$

Take out common factor x:

$7x(x - 5) = 0$

Apply zero product property:

$7x= 0 \ \ or \ \ x - 5 = 0$

Find value of x:

$x = 0 \ \ or \ \ x = 5$

,

Answer: x = 0 or x = 5

.

If x = 0

$\text{Fraction =} \dfrac{2(0) + 1}{3(0) - 2} = -\dfrac{1}{2}$

If x = 5

$\text{Fraction =} \dfrac{2(5) + 1}{3(5) - 2} = \dfrac{11}{13}$

.

Answer: The fraction is -1/2 or 11/13