Question

how to solve this?
$\frac{3}{2x - y} + \frac{8}{x + 2y} = 3$
how to solve this?
$\frac{12}{x + 2y} - \frac{6}{2x - y} = 1$

Answer 1

Given,

(3/2x-y)+(8/x+2y)=3

and,(12/x+2y)-(6/2x-y)=1

Let,(1/2x-y)=u

and, (1/x+2y)=v

So,3u+8v=3                       ............Eq.(1)

Also,12v-6u=1                    ............Eq.(2)

Multiplying Eq.(1) by 2

So, 6u+16v=6                     ............Eq.(3)

Adding Eq.(2) and Eq.(3)

   28v=7

So, v=1/4

Substituiting The value of v into Eq.(1)

   =>3u+8(1/4)=3

   =>3u+2=3

   =>3u=1

So, u=1/3

We assumed that (1/x+2y)=v and we got v=1/4

=>1/x+2y=1/4

=>x+2y=4                ................Eq.(4)

We assumed also that (1/2x-y)=u and we got u=1/3

=>1/2x-y=1/3

=>2x-y=3                  ................Eq.(5)

Multiplying Eq.(5) by 2

=>4x-2y=6                .................Eq.(6)

Adding Eq.(4) and Eq.(6)

=>5x=10

So, x=2

Subtituiting The value of x into Eq.(5)

2(2)-y=3

=>4-y=3

=>y=1

Thanks!!!