Solve the equation. 8-\frac{5}{x}=2+\frac{3}{x}

lwfrgin 2021-10-01 Answered
Solve the equation.
\(\displaystyle{8}-{\frac{{{5}}}{{{x}}}}={2}+{\frac{{{3}}}{{{x}}}}\)

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Expert Answer

smallq9
Answered 2021-10-02 Author has 21014 answers
Step 1
Given: \(\displaystyle{8}-{\frac{{{5}}}{{{x}}}}={2}+{\frac{{{3}}}{{{x}}}}\)
To solve- The above equation.
Step 2
Explanation- Rewrite the given expression,
\(\displaystyle{8}-{\frac{{{5}}}{{{x}}}}={2}+{\frac{{{3}}}{{{x}}}}\)
Simplifying the above expression transfering the x-term from right hand side to left hand side and constant term from left hand side to right hand side, we get,
\(\displaystyle-{\frac{{{3}}}{{{x}}}}-{\frac{{{5}}}{{{x}}}}={2}-{8}\)
\(\displaystyle{\frac{{-{3}-{5}}}{{{x}}}}=-{6}\)
\(\displaystyle{\frac{{-{8}}}{{{x}}}}=-{6}\)
Further simplify the above expression, we get,
\(\displaystyle{x}={\frac{{-{8}}}{{-{6}}}}\)
\(\displaystyle{x}={\frac{{{4}}}{{{3}}}}\)
Answer- Hence, the solution of the expression \(\displaystyle{8}-{\frac{{{5}}}{{{x}}}}={2}+{\frac{{{3}}}{{{x}}}}\ {i}{s}\ {x}={\frac{{{4}}}{{{3}}}}\).
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