Question

2(2x+3/x-3)-25(x-3/2x+3) = 5

Answer 1

Hello,
2(2x+3/x-3)-25(x-3/2x+3)=5
we bring both members to a common factor:
2(2x+3)(2x+3)-25(x-3)(x-3)/(x-3)(2x+3)=5(x-3)(2x+3)/(x-3)(2x+3)
we multiply both members by (x-3)(2x+3) in order to eliminate the denominator:
(x-3)(2x+3)× 2(2x+3)(2x+3)-25(x-3)(x-3)/(x-3)(2x+3)=5(x-3)(2x+3)/(x-3)(2x+3)×(x-3)(2x+3);
2(2x+3)(2x+3)-25(x-3)(x-3)=5(x-3)(2x+3);
2(4x²+12x+9)-25(x²-6x+9)=5(2x²+3x-6x-9);
8x²+24x+18-25x²+150x-225=5(2x²-3x-9);
-17x²+174x-207=10x²-15x-45;
-17x²+174x-207-10x²+15x+45=0;
-27x²+189x-162=0;
27x²-189x+162=0;
let's divide by 27:
x²-7x+6=0;
you can write as:
x²-6x-x+6=0;
x(x-6)-1(x-6)=0;
(x-1)(x-6)=0
then:
x-1=0; x=1
or
x-6=0; x=6

Bye :-)

Answer 2

hope this answer help you!!!