Question

⑤ $\frac{x - 1}{4xy^{3}}cdot\frac{6x^{2}y}{1 - x}$

Explanation:

Step1: Rewrite the second - fraction

We know that \(1 - x=-(x - 1)\). So the expression \(\frac{x - 1}{4xy^{3}}\cdot\frac{6x^{2}y}{1 - x}\) can be rewritten as \(\frac{x - 1}{4xy^{3}}\cdot\frac{6x^{2}y}{-(x - 1)}\).

Step2: Cancel out common factors

Cancel out the common factor \((x - 1)\) in the numerator and denominator. Also, simplify the coefficients and the variables. The \(x\) in the numerator and denominator: \(\frac{x^{2}}{x}=x\), and the \(y\) in the numerator and denominator: \(\frac{y}{y^{3}}=\frac{1}{y^{2}}\). The coefficients \(\frac{6}{4}=\frac{3}{2}\).
The simplified expression is \(\frac{1}{4xy^{3}}\cdot\frac{6x^{2}y}{- 1}=-\frac{3x}{2y^{2}}\).

Answer:

\(-\frac{3x}{2y^{2}}\)