Question

plz give a detailed answer of this question​

Answer 1

Answer:

x = -10  or  x = -1/5 .

Step-by-step explanation:

We are given the following expression;

                        $2(\frac{2x-1}{x+3}) - 3(\frac{x+3}{2x-1}) = 5$

                         $\frac{2(2x-1)^{2} - 3(x+3)^{2} }{(x+3)(2x-1)} = 5$

                         $\frac{2(4x^{2}+1 -4x) - 3(x^{2} +9-6x) }{(2x^{2}+5x-3 )} = 5$      

                          $\frac{8x^{2}+2 -8x - 3x^{2} -27-18x }{(2x^{2}+5x-3 )} = 5$

                        $8x^{2}+2 -8x - 3x^{2} -27-18x = 5* (2x^{2}+5x-3 )$    

                        $8x^{2}+2 -8x - 3x^{2} -27-18x = 10x^{2}+25x-15$

                        $5x^{2} -26x-25 = 10x^{2}+25x-15$    

                        $10x^{2}+25x-15 - 5x^{2} +26x+25 = 0$

                        $5x^{2} +51x+10 = 0$  

Now we will solve this equation using middle term splitting method;

                        $5x^{2} +50x+x+10 = 0$

                        $5x(x+10)+1(x+10) = 0$

                         $(5x+1)(x+10) = 0$    

This means either $5x+1 =0$  or   $x+10 = 0$

i.e.  x = -1/5  or  x = -10.