Question
Subtract the rational expressions. \[ \frac{x^{2}-x}{7 x}-\frac{9 x^{2}-x}{7 x} \]
Ask by O'Quinn Vaughn. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \(-\frac{8x}{7}\).
Solution
Calculate or simplify the expression \( (x^{2}-x)/7x-(9x^{2}-x)/7x \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(x^{2}-x\right)}{7x}-\frac{\left(9x^{2}-x\right)}{7x}\)
- step1: Remove the parentheses:
\(\frac{x^{2}-x}{7x}-\frac{9x^{2}-x}{7x}\)
- step2: Divide the terms:
\(\frac{x-1}{7}-\frac{9x^{2}-x}{7x}\)
- step3: Divide the terms:
\(\frac{x-1}{7}-\frac{9x-1}{7}\)
- step4: Transform the expression:
\(\frac{x-1-\left(9x-1\right)}{7}\)
- step5: Subtract the terms:
\(\frac{-8x}{7}\)
- step6: Rewrite the fraction:
\(-\frac{8x}{7}\)
The result of subtracting the rational expressions is \(-\frac{8x}{7}\).
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Simplify this solution Bonus Knowledge
To subtract the given rational expressions, we first notice that they have a common denominator of \( 7x \). We can combine the numerators directly. The expressions are: \[ \frac{x^{2}-x}{7x} - \frac{9x^{2}-x}{7x} \] By subtracting the numerators, we get: \[ \frac{(x^{2}-x) - (9x^{2}-x)}{7x} \] Simplifying the numerator: \[ (x^{2} - x) - (9x^{2} - x) = x^{2} - x - 9x^{2} + x = x^{2} - 9x^{2} - x + x = -8x^{2} \] So, we can now write: \[ \frac{-8x^{2}}{7x} \] To simplify this further, we can divide \( -8x^{2} \) by \( 7x \): \[ \frac{-8x^{2}}{7x} = \frac{-8x}{7} \] Thus, the final result of the subtraction is: \[ \frac{-8x}{7} \]
