Question
Simplify the expression. \( \frac{2 x^{2}+x-1}{x+1} \) \( \frac{2 x^{2}+x-1}{x+1}=\square \) (Simplify your answer.)
Ask by Hanson Powers. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(2x - 1\).
Solution
Calculate or simplify the expression \( (2x^2+x-1)/(x+1) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(2x^{2}+x-1\right)}{\left(x+1\right)}\)
- step1: Remove the parentheses:
\(\frac{2x^{2}+x-1}{x+1}\)
- step2: Factor the expression:
\(\frac{\left(x+1\right)\left(2x-1\right)}{x+1}\)
- step3: Reduce the fraction:
\(2x-1\)
The simplified expression is \(2x-1\).
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Simplify this solution Extra Insights
To simplify the expression \( \frac{2x^2 + x - 1}{x + 1} \), we start by factoring the numerator. The quadratic expression \( 2x^2 + x - 1 \) can be factored as \( (2x - 1)(x + 1) \). So we have: \[ \frac{2x^2 + x - 1}{x + 1} = \frac{(2x - 1)(x + 1)}{x + 1} \] Now we can cancel out \( x + 1 \) from the numerator and the denominator, provided \( x \neq -1 \): \[ = 2x - 1 \] Thus, the simplified expression is: \[ \frac{2x^2 + x - 1}{x + 1} = 2x - 1 \quad (x \neq -1) \]
