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

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

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Steacensen69
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
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