Question

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

Please solve.
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Answer 1

ANSWER:

Given:

• (x + 3)/(x - 2) - (1 - x)/x = 17/4

To Find:

• Value of x

Solution:

We are given that,

$\implies\sf\dfrac{x+3}{x-2}-\dfrac{1-x}{x}=\dfrac{17}{4}$

On taking LCM in LHS,

$\implies\sf\dfrac{(x+3)(x)-(1-x)(x-2)}{(x)(x-2)}=\dfrac{17}{4}$

So,

$\implies\sf\dfrac{(x^2+3x)-(x-x^2-2+2x)}{x^2-2x}=\dfrac{17}{4}$

On simplifying,

$\implies\sf\dfrac{x^2+3x-x+x^2+2-2x}{x^2-2x}=\dfrac{17}{4}$

Solving like terms,

$\implies\sf\dfrac{2x^2+2}{x^2-2x}=\dfrac{17}{4}$

On cross-multiplying,

$\implies\sf4(2x^2+2)=17(x^2-2x)$

Hence,

$\implies\sf8x^2+8=17x^2-34x$

Transposing LHS to RHS,

$\implies\sf0=17x^2-34x-8x^2-8$

Hence,

$\implies\sf9x^2-34x-8=0$

On splitting the middle term,

$\implies\sf9x^2-36x+2x-8=0$

Taking common,

$\implies\sf9x(x-4)+2(x-4)=0$

Taking (x - 4) common,

$\implies\sf(x-4)(9x+2)=0$

So,

$\implies\sf x-4=0\:\:\:and\:\:\:9x+2=0$

Therefore,

$\implies\bf x=4\:\:\:and\:\:\:x=\dfrac{-2}{9}$