Solve the rational equation. \frac{7}{x}+x=\frac{88}{x}

IMLOG10ct 2021-11-21 Answered
Solve the rational equation.
\(\displaystyle{\frac{{{7}}}{{{x}}}}+{x}={\frac{{{88}}}{{{x}}}}\)

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Expert Answer

Steacensen69
Answered 2021-11-22 Author has 1470 answers
Step 1
In first step, simplify the equation to form a more specific form where variables are on one side and constant values on the other side of equality as.
\(\displaystyle{\frac{{{7}}}{{{x}}}}+{x}={\frac{{{88}}}{{{x}}}}\)
multiply by x on both sides of equation;
\(\displaystyle{\left({\frac{{{7}}}{{{x}}}}+{x}\right)}{x}={\left({\frac{{{88}}}{{{x}}}}\right)}{x}\)
\(\displaystyle{7}+{x}^{{{2}}}={88}\)
\(\displaystyle{x}^{{{2}}}={88}-{7}\)
\(\displaystyle{x}^{{{2}}}={81}\)
Step 2
Now solve for x, to get the desired values as.
\(\displaystyle{x}^{{{2}}}={81}\)
\(\displaystyle{x}=\pm\sqrt{{{81}}}\)
\(\displaystyle{x}=\pm{9}\)
x=9, -9
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Uersfeldte
Answered 2021-11-23 Author has 1353 answers
Step 1: Find the common denominator
\(\displaystyle{\frac{{{7}}}{{{x}}}}+{x}={\frac{{{88}}}{{{x}}}}\)
\(\displaystyle{\frac{{{7}}}{{{x}}}}+{\frac{{\times}}{{{x}}}}={\frac{{{88}}}{{{x}}}}\)
Step 2: Add fractions with a common denominator
\(\displaystyle{\frac{{{7}+\times}}{{{x}}}}={\frac{{{88}}}{{{x}}}}\)
Step 3: Group degrees
\(\displaystyle{\frac{{{7}+{x}^{{{2}}}}}{{{x}}}}={\frac{{{88}}}{{{x}}}}\)
Step 4: Rearrange the terms of the equation
\(\displaystyle{\frac{{{x}^{{{2}}}+{7}}}{{{x}}}}={\frac{{{88}}}{{{x}}}}\)
Step 5: Multiply all terms by the same number to get rid of the denominators
\(\displaystyle{x}{\left({\frac{{{x}^{{{2}}}+{7}}}{{{x}}}}\right)}={x}\cdot{\frac{{{88}}}{{{x}}}}\)
Step 6: Reduce the multiplied terms in the denominator
\(\displaystyle{x}^{{{2}}}+{7}={88}\)
Step 7: Move the terms to the left of the equation
\(\displaystyle{x}^{{{2}}}+{7}-{88}={0}\)
Step 8: Subtract the numbers
\(\displaystyle{x}^{{{2}}}-{81}={0}\)
Step 9: Use the sum of the products
\(\displaystyle{x}^{{{2}}}-{81}={0}\)
Step 10: Multiply by factors
(x-9)(x+9)=0
Step 11: Create two separate equations
x-9=0
x+9=0
Step 12: Calculation
x=9
x=-9
The solution
x=9
x=-9
0

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