Question
Divide. \[ \frac{10 x^{2} y^{2}+30 x y^{2}-10 y^{2}}{5 x^{2} y} \]
Ask by Paul Conner. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{2yx^{2}+6yx-2y}{x^{2}} \).
Solution
Calculate or simplify the expression \( \frac{10x^2y^2+30xy^2-10y^2}{5x^2y} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{10x^{2}y^{2}+30xy^{2}-10y^{2}}{5x^{2}y}\)
- step1: Factor:
\(\frac{5y\left(2yx^{2}+6yx-2y\right)}{5x^{2}y}\)
- step2: Reduce the fraction:
\(\frac{2yx^{2}+6yx-2y}{x^{2}}\)
The result of dividing \(10x^{2}y^{2}+30xy^{2}-10y^{2}\) by \(5x^{2}y\) is \(\frac{2yx^{2}+6yx-2y}{x^{2}}\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify the expression \[ \frac{10 x^{2} y^{2}+30 x y^{2}-10 y^{2}}{5 x^{2} y}, \] we first factor the numerator. Notice that we can factor out \(10y^2\) from the terms in the numerator: \[ 10 x^{2} y^{2} + 30 x y^{2} - 10 y^{2} = 10 y^{2} (x^{2} + 3x - 1). \] Now, substituting this back in, we have: \[ \frac{10 y^{2} (x^{2} + 3x - 1)}{5 x^{2} y}. \] Next, we can simplify further. The \(10\) in the numerator and the \(5\) in the denominator reduce: \[ \frac{10}{5} = 2, \] leading to: \[ \frac{2 y (x^{2} + 3x - 1)}{x^{2}}. \] Thus, the final simplified form of the given expression is: \[ \frac{2 y (x^{2} + 3x - 1)}{x^{2}}. \]
