Multiply and simplify the rational expression: (2x3y)⋅(6y−4x)

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Tuthornt · Accepted Answer

To multiply two rational expressions, we should first cancel any common factors.
The numerator of the first fraction and denominator of the second fraction have a common factor of x so we can cancel the xs:
$(2 \frac{x}{3} y) \cdot (6 \frac{y}{4} x) = (\frac{2}{3} y) \cdot (6 \frac{y}{4})$
The denominator of the first fraction and numerator of the second fraction have a common factor of y so we can cancel the ys:
$(\frac{2}{3} y) \cdot (6 \frac{y}{4}) = (\frac{2}{3}) \cdot (\frac{6}{4})$
The 2 and 4 have a common factor of 2 so divide them both by 2:
$(\frac{2}{3}) \cdot (\frac{6}{4}) = (\frac{2}{3}) \cdot (\frac{6}{4})$
The 3 and 6 have a common factor of 3 so divide them both by 3:
$(\frac{1}{3}) \cdot (\frac{6}{2}) = (\frac{1}{1}) \cdot (\frac{2}{2})$
Since $\frac{1}{1} = 1$ and $\frac{2}{2} = 1$ , then:
$(\frac{1}{1}) \cdot (\frac{2}{2}) = 1 \cdot 1 = 1$

Multiply and simplify the rational expression: (2x/3y)*(6y-4x)

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