Question

Solve for x if 1/2x-3 + 5x/2x+6 =2​

Answer 1

Answer:

by which method do you need

Answer 2

The value of x is "$\bold{(2, \frac{21}{2})}$".

Given:

$\to \frac{1}{2x-3} + \frac{5x}{2x+6} =2$

To find:

x=?

Solution:

$\to \frac{1}{2x-3} + \frac{5x}{2x+6} =2$

Taking lcm:

$\to \frac{2x+6 +5x(2x-3)}{(2x-3)(2x+6)} =2\\\\\to \frac{2x+6 +10x^2- 15x}{(4x^2+ 12x-6x-18)} =2\\\\\to \frac{10x^2- 13x+6}{4x^2+ 6x-18} =2$

$\to 10x^2- 13x+6 = 2(4x^2+ 6x-18)\\\\\to 10x^2- 13x+6 = 8x^2+ 12x-36\\\\\to 10x^2- 13x+6 - 8x^2- 12x +36=0\\\\\to 2x^2-25x+42=0$

compare the value with the $ax^2+bx+c=0$:

$\to a=2\\\\\to b= -25\\\\\to c=42$

Using formula:

$\to \bold{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}$

       $\bold{=\frac{- (-25) \pm \sqrt{(-25)^2-4\times 2 \times 42}}{2 \times 2}}\\\\ \bold{=\frac{25 \pm \sqrt{ 625 - 336}}{4}}\\\\ \bold{=\frac{25 \pm \sqrt{289}}{4}}\\\\ \bold{=\frac{25 \pm 17 }{4}}\\\\ \bold{=(\frac{8}{4} , \frac{42}{4})}\\\\ \bold{=( 2 , \frac{21}{2})}$

Therefore, the final answer is "$\bold{(2, \frac{21}{2})}$".

Learn more about the value x:

brainly.com/question/18681264