Question

please help me fast as fast you can plz ​

Answer 1

Answer:

Hi there, here I have pinned the answer below.

Hope this helps.

All the best.

Answer 2

Given :

• $\bf\:2(\frac{3x-5}{x+2})-5(\frac{x+2}{3x-5})=3$

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To find :

• The value of x

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Assumption :

Let -

• $\sf\:\frac{3x-5}{x+2}$ be $\bf\:a$
• $\sf\:\frac{x+2}{3x-5}$ be $\bf\:\frac{1}{a}$

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Solution :

$\sf\:2(\frac{3x-5}{x+2})-5(\frac{x+2}{3x-5})=3$

Now substituting the assumed values

$\sf\implies\:2a-5(\frac{1}{a})=3$

Multiplying the terms

$\sf\implies\:2a-\frac{5}{a}=3$

Solving further

$\sf\implies\:\frac{2a^{2}-5}{a}=3$

Cross multiplying

$\sf\implies\:2a^{2}-5=3a$

$\sf\implies\:2a^{2}-3a-5=0$

$\sf\implies\:2a^{2}-(5-2)a-5=0$

$\sf\implies\:2a^{2}-5a+2a-5=0$

$\sf\implies\:a(2a-5)+1(2a-5)=0$

$\sf\implies\:(2a-5)(a+1)=0$

$\large{\mathfrak\red{\therefore~a~=~\frac{5}{2}}}$ and $\large{\mathfrak\red{~a~=~-1}}$

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Substituting back the value of a and 1/a we get

$\sf\:\frac{3x-5}{x+2}=\frac{5}{2}$

and

$\sf\:\frac{x+2}{3x-5}=-1$

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Solving

$\sf\:\frac{3x-5}{x+2}=\frac{5}{2}$

$\sf\longrightarrow\:2(3x-5)=5(x+2)$

$\sf\longrightarrow\:6x-10=5x+10$

$\sf\longrightarrow\:6x-5x=10+10$

$\sf\longrightarrow\:1x=20$

$\small{\underline{\boxed{\mathrm{\longrightarrow~x~=~20}}}}$

and

$\sf\:\frac{x+2}{3x-5}=-1$

$\sf\longrightarrow\:x+2=-1(3x-5)$

$\sf\longrightarrow\:x+2=-3x+10$

$\sf\longrightarrow\:x+3x=10-2$

$\sf\longrightarrow\:4x=8$

$\sf\longrightarrow\:x=\frac{8}{4}$

$\sf\longrightarrow\:x=\cancel{\frac{8}{4}}$

$\small{\underline{\boxed{\mathrm{\longrightarrow~x~=~2}}}}$

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