Carlson Parry
01/05/2024 · Senior High School
Simplify the complex fraction. \[ \frac{2+\frac{1}{x}-\frac{15}{x^{2}}}{3+\frac{10}{x}+\frac{3}{x^{2}}} \]
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( (2+1/x-15/x^2)/(3+10/x+3/x^2) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(2+\frac{1}{x}-\frac{15}{x^{2}}\right)}{\left(3+\frac{10}{x}+\frac{3}{x^{2}}\right)}\)
- step1: Remove the parentheses:
\(\frac{2+\frac{1}{x}-\frac{15}{x^{2}}}{3+\frac{10}{x}+\frac{3}{x^{2}}}\)
- step2: Calculate:
\(\frac{\frac{2x^{2}+x-15}{x^{2}}}{3+\frac{10}{x}+\frac{3}{x^{2}}}\)
- step3: Add the terms:
\(\frac{\frac{2x^{2}+x-15}{x^{2}}}{\frac{3x^{2}+10x+3}{x^{2}}}\)
- step4: Multiply by the reciprocal:
\(\frac{2x^{2}+x-15}{x^{2}}\times \frac{x^{2}}{3x^{2}+10x+3}\)
- step5: Rewrite the expression:
\(\frac{\left(x+3\right)\left(2x-5\right)}{x^{2}}\times \frac{x^{2}}{\left(x+3\right)\left(3x+1\right)}\)
- step6: Reduce the fraction:
\(\left(2x-5\right)\times \frac{1}{3x+1}\)
- step7: Multiply the terms:
\(\frac{2x-5}{3x+1}\)
The simplified form of the complex fraction \[ \frac{2+\frac{1}{x}-\frac{15}{x^{2}}}{3+\frac{10}{x}+\frac{3}{x^{2}}} \] is \[ \frac{2x-5}{3x+1} \].
Quick Answer
\[ \frac{2x-5}{3x+1} \]
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