Question

please solve question fast​

Answer 1

Answer:-

The Required Values of x are 0, 1 and 2.

Explanation:-

Given:-

• $\bf\dfrac{x+3}{x-1}>x.$

And we have to find out the value of x.

So,

By simplifying the above equation we can get the value of x:-

$\\ \tt\mapsto\dfrac{x+3}{x-1} > x.$

$\\ \tt\mapsto x + 3 > x(x - 1).$

$\\ \tt\mapsto x + 3 > {x}^{2} - x.$

$\\ \tt\mapsto0 > {x}^{2} - x -( x + 3).$

$\\ \tt\mapsto {x}^{2} - x - x - 3 < 0 \: \: \: \: \rm(by \: ope ning \: brackets).$

$\\ \tt\mapsto {x}^{2} - 2x - 3 < 0.$

By Splitting Middle Term:-

$\\ \tt\mapsto {x}^{2} - (3 - 1)x - 3 < 0.$

$\\ \tt\mapsto {x}^{2} - 3x + x - 3 < 0.$

$\\ \tt\mapsto x(x - 3) + 1(x - 3) < 0.$

$\\ \tt\mapsto (x - 3)(x +1) < 0.$

$\\ \rm \mapsto \: either \: \: x - 3 < 0 \: \: \: \: or \: \: \: \: x + 1 < 0.$

$\\ \rm\mapsto \: either \: \: x < 3 \: \: \: \: or \: \: \: \: x < - 1.$

So the required valus of x are between -1 and 3 which are 0, 1, 2.

Therefore,

There are three values of x possible:-

• 0.
• 1.
• 2.

Therefore required values of x are 0, 1 and 2.