Question

solve for x : 2(x+2/2x-3)-9(2x-3/x+2)=3; x≠-2,3/2

Answer 1

now u can solve it further

Answer 2

Answer:

Values of x are 2.2 and 0.625

Step-by-step explanation:

Given:

$2(\frac{x+2}{2x-3})-9(\frac{2x-3}{x+2})=3$

To find: Value of x

Consider,

$2(\frac{x+2}{2x-3})-9(\frac{2x-3}{x+2})=3$

$\frac{2(x+2)(x+2)-9(2x-3)(2x-3)}{(2x-3)(x+2)}=3$

$2(x+2)^2-9(2x-3)^2=3(2x-3)(x+2)$

$2(x^2+4+4x)-9(4x^2+9-12x)=3(2x^2-6+x)$

$2x^2+8+8x-36x^2-81+108x=6x^2-18+3x$

$2x^2-36x^2-6x^2+8x+108x-3x-81+8+18=0$

$-40x^2+113x-55=0$

$40x^2-113x+55=0$

Now we solve this by using Quadratic Formula,

$x=\frac{-(-113)\pm\sqrt{(-113)^2-4(40)(55)}}{2(40)}$

$x=\frac{113\pm\sqrt{12769-8800}}{80}$

$x=\frac{113\pm\sqrt{3969}}{80}$

$x=\frac{113\pm63}{80}$

$x=\frac{113+63}{80}\;\:and\;\:x=\frac{113-63}{80}$

$x=\frac{176}{80}\;\:and\;\:x=\frac{50}{80}$

$x=2.2\;\:and\;\:x=0.625$

Therefore, Values of x are 2.2 and 0.625