Question

solve 3[2x+3/x-3]-25[x-3/2x+3]=5​

Answer 1

Answer:

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

Explanation: