Q14. - Algebra 1

Question

Find the product.

$\frac{\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{5}\mathbf{)}\mathbf{(}\mathbf{x}\mathbf{-}\mathbf{3}\mathbf{)}}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{.}\frac{\mathbf{5}\mathbf{x}}{\mathbf{x}\mathbf{-}\mathbf{3}}$

Step-by-Step Solution

Answer

The final answer is $\frac{\mathbf{5}\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{5}\mathbf{)}}{{\mathbf{x}}^{\mathbf{2}}}$.

Step 1. Define a rational function.

A function of the form $y=\frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q\ne 0$.

Step 2. Define the product of two expressions a b and c d .

The product of two expressions $\frac{a}{b}$ and $\frac{c}{d}$, where $b\ne 0$ and $d\ne 0$, is given below.

$\frac{a}{b}.\frac{c}{d}=\frac{ac}{bd}\mathrm{...........}\left(1\right)$

Step 3. Calculate the product ( x + 5 ) ( x − 3 ) x 3 . 5 x x − 3 .

Use $\left(1\right)$ to find the product $\frac{(x+5)(x-3)}{x^3}.\frac{5x}{x-3}$.

$\begin{array}{l}\frac{(x+5)(x-3)}{x^3}.\frac{5x}{x-3}=\frac{(x+5)(x-3)\left(5x\right)}{x^3(x-3)}\\ =\frac{5(x+5)}{x^2}\end{array}$

Therefore, the final answer is $\frac{5(x+5)}{x^2}$.