Question
Subtract. \( \quad \frac{7}{x}-\frac{6}{x+1} \) Simplify your answer as much as possible.
Ask by Gibson Bryant. in the United States
Dec 09,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \frac{x+7}{x^{2}+x} \)
Solution
Calculate or simplify the expression \( 7/x-6/(x+1) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{7}{x}-\frac{6}{\left(x+1\right)}\)
- step1: Remove the parentheses:
\(\frac{7}{x}-\frac{6}{x+1}\)
- step2: Reduce fractions to a common denominator:
\(\frac{7\left(x+1\right)}{x\left(x+1\right)}-\frac{6x}{\left(x+1\right)x}\)
- step3: Rewrite the expression:
\(\frac{7\left(x+1\right)}{x\left(x+1\right)}-\frac{6x}{x\left(x+1\right)}\)
- step4: Transform the expression:
\(\frac{7\left(x+1\right)-6x}{x\left(x+1\right)}\)
- step5: Multiply the terms:
\(\frac{7x+7-6x}{x\left(x+1\right)}\)
- step6: Subtract the terms:
\(\frac{x+7}{x\left(x+1\right)}\)
- step7: Multiply the terms:
\(\frac{x+7}{x^{2}+x}\)
The simplified form of \( \frac{7}{x}-\frac{6}{x+1} \) is \( \frac{x+7}{x^{2}+x} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To subtract the fractions \( \frac{7}{x} - \frac{6}{x+1} \), we need a common denominator, which is \( x(x+1) \). Now we rewrite each fraction with the common denominator: \[ \frac{7}{x} = \frac{7(x+1)}{x(x+1)} = \frac{7x + 7}{x(x+1)} \] \[ \frac{6}{x+1} = \frac{6x}{x(x+1)} = \frac{6x}{x(x+1)} \] Now, we can perform the subtraction: \[ \frac{7x + 7}{x(x+1)} - \frac{6x}{x(x+1)} = \frac{(7x + 7) - 6x}{x(x+1)} \] This simplifies to: \[ \frac{7x + 7 - 6x}{x(x+1)} = \frac{x + 7}{x(x+1)} \] Thus, the simplified answer is: \[ \frac{x + 7}{x(x+1)} \]
