# How to solve :-1/2a+b+2x=1/2a+1/b+1/2x ?

Welcome to my article How to solve :-1/2a+b+2x=1/2a+1/b+1/2x ?. This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
For complete information on how to solve this question How to solve :-1/2a+b+2x=1/2a+1/b+1/2x ?, read and understand it carefully till the end.

Let us know how to solve this question How to solve :-1/2a+b+2x=1/2a+1/b+1/2x ?

First write the question on the page of the notebook.

1/2a+b+2x=1/2a+1/b+1/2x ?

By writing this question correctly in this way,

\displaystyle \frac{1}{{\left( {2a+b+2x} \right)}}=\frac{1}{{2a}}+\frac{1}{b}+\frac{1}{{2x}} ,

\displaystyle \frac{1}{{\left( {2a+b+2x} \right)}}-\frac{1}{{2x}}=\frac{1}{{2a}}+\frac{1}{b} ,

\displaystyle \frac{1}{{\left( {2a+b+2x} \right)}}-\frac{1}{{2x}}=\frac{{b+2a}}{{2ab}} ,

\displaystyle \frac{{2x\times 1-1\times \left( {2a+b+2x} \right)}}{{\left( {2a+b+2x} \right)\times 2x}}=\frac{{b+2a}}{{2ab}} ,

\displaystyle \frac{{2x-2a-b-2x}}{{\left( {2a+b+2x} \right)\times 2x}}=\frac{{b+2a}}{{2ab}} ,

\displaystyle \frac{{2x-2a-b-2x}}{{2a\times 2x+b\times 2x+2x\times 2x}}=\frac{{b+2a}}{{2ab}} ,

\displaystyle \frac{{2x-2a-b-2x}}{{4ax+2bx+4{{x}^{2}}}}=\frac{{b+2a}}{{2ab}} ,

\displaystyle \frac{{2x-2x-2a-b}}{{4ax+2bx+4{{x}^{2}}}}=\frac{{b+2a}}{{2ab}} ,

\displaystyle \frac{{-2a-b}}{{4ax+2bx+4{{x}^{2}}}}=\frac{{b+2a}}{{2ab}} ,

\displaystyle 2ab\times \left( {-2a-b} \right)=\left( {b+2a} \right)\times \left( {4ax+2bx+4{{x}^{2}}} \right) ,

or,

\displaystyle 2ab\times -\left( {2a+b} \right)=\left( {2a+b} \right)\times \left( {4ax+2bx+4{{x}^{2}}} \right) ,

\displaystyle \frac{{2ab\times -\left( {2a+b} \right)}}{{\left( {2a+b} \right)}}=\left( {4ax+2bx+4{{x}^{2}}} \right) ,

\displaystyle 2ab\times -1=\left( {4ax+2bx+4{{x}^{2}}} \right) ,

\displaystyle -2ab=4ax+2bx+4{{x}^{2}} ,

\displaystyle 0=4ax+2bx+4{{x}^{2}}+2ab ,

or,

\displaystyle 4ax+2bx+4{{x}^{2}}+2ab=0 ,

\displaystyle 4{{x}^{2}}+2bx+4ax+2ab=0 ,

\displaystyle 2x\left( {2x+b} \right)+2a\left( {2x+b} \right)=0 ,

\displaystyle \left( {2x+b} \right)\left( {2x+2b} \right)=0 ,

if, 2x + b = 0

2x = – b

if, 2x + 2b = 0

2x = -2b

x = -2b/2

## x = -b

Or in this way after solving this question line by line, its intended solution,

## x = -b/2 and -b [Answer]

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