Question

Plz try to solve this my brain is very tried to solve this question I hope You will do it plz plz solve this by only cross multiplication method class 10th chapter 3rd.
I will marked you brainlist plz plz plz solve this ​

Answer 1

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

$\small{\frac{1}{3x+y}(3x+y)+\frac{1}{3x-y}(3x+y)=\frac{3}{4}(3x + y)}$

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

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

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

$4+\frac{4(3x+y)}{3x-y}=3(3x+y)$

$4+\frac{4(3x+y)}{3x-y}=9x+3y$

$\frac{4(3x+y)}{3x-y}=9x+3y-4$

4(3x+y)=(9x+3y−4)(3x−y)

$12x+4y=27{x}^{2}-9xy+9yx-3{y}^{2}-12x+4y$

$12x+4y=27{x}^{2}-3{y}^{2}-12x+4y$

$12x=27{x}^{2}-3{y}^{2}-12x$

$12x-27{x}^{2}+3{y}^{2}+12x=0$

$24x-27{x}^{2}+3{y}^{2}=0$

$x=\frac{-24+6\sqrt{16+9{y}^{2}}}{-54},\frac{-24-6\sqrt{16+9{y}^{2}}}{-54}$

$x=\frac{4-\sqrt{16+9{y}^{2}}}{9},\frac{4+\sqrt{16+9{y}^{2}}}{9}$