Solve the equation. \frac{3}{2x+5}+\frac{4}{2x-5}=\frac{14x+3}{4x^{2}-25

Phoebe 2021-09-19 Answered
Solve the equation.
\(\displaystyle{\frac{{{3}}}{{{2}{x}+{5}}}}+{\frac{{{4}}}{{{2}{x}-{5}}}}={\frac{{{14}{x}+{3}}}{{{4}{x}^{{{2}}}-{25}}}}\)

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Expert Answer

svartmaleJ
Answered 2021-09-20 Author has 17461 answers
Step 1
Given:
\(\displaystyle{\frac{{{3}}}{{{2}{x}+{5}}}}+{\frac{{{4}}}{{{2}{x}-{5}}}}={\frac{{{14}{x}+{3}}}{{{4}{x}^{{{2}}}-{25}}}}\)
Now we simplify the above equation as,
\(\displaystyle\Rightarrow{\frac{{{3}{\left({2}{x}-{5}\right)}+{4}{\left({2}{x}+{5}\right)}}}{{{4}{x}^{{{2}}}-{25}}}}={\frac{{{14}{x}+{3}}}{{{4}{x}^{{{2}}}-{25}}}}\)
\(\displaystyle\Rightarrow{\frac{{{6}{x}-{15}+{8}{x}+{20}}}{{{4}{x}^{{{2}}}-{25}}}}={\frac{{{14}{x}+{3}}}{{{4}{x}^{{{2}}}-{25}}}}\)
\(\displaystyle\Rightarrow{14}{x}+{5}={14}{x}+{3}\)
\(\displaystyle\Rightarrow{5}={3}\)
Step 2
Which is not possible.
Since,
\(\displaystyle{5}\ne{3}\)
Therefore equation has no solution
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