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For all values of x for which the expression is defined, perform the indicated operation and...

Question:

For all values of {eq}x {/eq} for which the expression is defined, perform the indicated operation and express in simplest form.

{eq}\displaystyle\; \frac{x^{2} + 3x - 4}{5x - 4} \times \frac{10x^{2} - 40x}{x^{2} - 16} {/eq}

Multiplication:

Algebraic multiplication is done using the distributive property. However, generally, when we are multiplying algebraic fractions, we can first factorize them to remove all common terms of the numerators and denominators.

Answer and Explanation:


The operation indicated is performed as follows.


$$\begin{align} \frac{x^{2} + 3x - 4}{5x - 4} \times \frac{10x^{2} - 40x}{x^{2} - 16} &=\frac{x^2+4x-x-4}{5x-4} \times \frac{10x(x-4)}{x^2-4^2}\\[0.3cm] &=\frac{x(x+4)-(x+4)}{5x-4} \times \frac{10x(x-4)}{(x+4)(x-4)}\\[0.3cm] &=\frac{(x-1)(x+4)}{5x-4} \times \frac{10x(x-4)}{(x+4)(x-4)}\\[0.3cm] &=\frac{10x(x-1)}{5x-4} \end{align} $$


Learn more about this topic:

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