Question

x+3/x-2 - 1-x/x=17/4,x is not equal to 0,2.
help me guyss please!!!!​

Answer 1

Answer:

4 and -2/9

Step-by-step explanation:

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

On taking the LCM for the denominators and solving,

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

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

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

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

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

$4(2 {x}^{2} + 2) = 17( {x}^{2} - 2x)$

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

$17 {x}^{2} - 8 {x}^{2} - 34x - 8 = 0$

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

On factorization and solving, we have,

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

So,

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

$x = 4 \: \: and \: \: x = - \frac{2}{9}$

Therefore, the required value is 4 and -2/9.

Hope it helps you.

Good Luck.