Question

the solution set of x+3/x-2 - 1-x/x = 17/4​

Answer 1

Step-by-step explanation:

4,\bold{\frac{-2}{9}}9−2 is the value of x if \bold{\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}.}x−2x+3−x1−x=417.

Given:

\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}x−2x+3−x1−x=417

To find:

The value of x=?

Solution:

To find the answer of the given terms  

\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}x−2x+3−x1−x=417

Take LCM  for the given terms  

\frac{(x+3)(x)-(x-2)(1-x)}{x(x-2)}=\frac{17}{4}x(x−2)(x+3)(x)−(x−2)(1−x)=417

Cross multiply both left side and right side  

\begin{gathered}\begin{array}{l}{4\left(x^{2}+3 x-\left(x-2-x^{2}+2 x\right)\right)=17\left(x^{2}-2 x\right)} \\ {4\left(x^{2}+3 x+x^{2}-3 x+2\right)=17 x^{2}-34 x} \\ {4\left(2 x^{2}+2\right)=17 x^{2}-34 x}\end{array}\end{gathered}4(x2+3x−(x−2−x2+2x))=17(x2−2x)4(x2+3x+x2−3x+2)=17x2−34x4(2x2+2)=17x2−34x

8 x^{2}+8=17 x^{2}-34 x8x2+8=17x2−34x

The quadratic equation is formed, find the roots of the quadratic equation  

\begin{gathered}\begin{array}{l}{9 x^{2}-34 x-8=0} \\ {9 x^{2}-36 x+2 x-8=0} \\ {9 x(x-4)+2(x-4)=0}\end{array}\end{gathered}9x2−34x−8=09x2−36x+2x−8=09x(x−4)+2(x−4)=0

The value of x by solving the quadratic equation is  

\begin{gathered}\begin{array}{l}{(x-4)(9 x+2)=0} \\ {x=4,-\frac{2}{9}}\end{array}\end{gathered}(x−4)(9x+2)=0x=4,−92

Therefore, x=4,\bold{\frac{-2}{9}}9−2 if  \frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}.}