Question

x+3/x-2 - 1-x/x = 17/4 solve quadratic equation by factorization method

Answer 1

Equation at the end of step  1  :

(x + 3) (1 - x) 17 (——————— - ———————) - —— = 0 (x - 2) x 4

Answer 2

Answer:

The roots of the given quadratic equation is $x=-\frac{2}{9},x=4$

Step-by-step explanation:

Given : Expression $\frac{x+3}{x-2}-\frac{1-x}{x}= \frac{17}{4}$

To solve : The quadratic equation by factorization method?

Solution :

$\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}$

Taking LCM,

$\frac{(x+3)x-(1-x)(x-2)}{x(x-2)}=\frac{17}{4}$

Cross multiply,

$4(x^2+3x-(x-2-x^2+2x))=17(x^2-2x)$

$4(x^2+3x-x+2+x^2-2x)=17(x^2-2x)$

$4(2x^2+2)=17x^2-34x$

$8x^2+8=17x^2-34x$

$9x^2-34x-8=0$

$9x^2-36x+2x-8=0$

$9x(x-4)+2(x-4)=0$

$(9x+2)(x-4)=0$

$(9x+2)=0,(x-4)=0$

$x=-\frac{2}{9},x=4$

Therefore, The roots of the given quadratic equation is $x=-\frac{2}{9},x=4$