Question

x+3/x-2 - 1-x/x = 17/4 solve by factorisation method

Answer 1

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

Given:

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

To find:

The value of x=?

Solution:

To find the answer of the given terms  

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

Take LCM  for the given terms  

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

Cross multiply both left side and right side  

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

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

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

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

The value of x by solving the quadratic equation is  

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

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

Answer 2

Answer:

Step-by-step explanation:

Solution :-

We have

(x + 3)/(x - 2) - (1 - x)/x = 17/4

⇒ x(x + 3) - (1 - x) (x - 2)/x(x - 2) = 17/4

⇒ 2x² + 2/x² - 2x = 17/4

⇒ 8x² + 8 = 17x² - 34x

⇒ 9x² - 34x - 8 = 0

By using factorization method, we get

⇒ 9x² - 36x + 2x - 8 = 0

⇒ 9x(x - 4) + 2(x - 4) = 0

⇒ (x - 4) (9x + 2) = 0

⇒ x - 4 = 0 or 9x + 2 = 0

⇒ x = 4, - 2/9 (As x can't be negative)

⇒ x = 4

But here, x = 4, - 2/9