Question

Which expression is equivalent to startfraction 3 x over x 1 endfractiondivided by x 1? startfraction 3 x over x 1 endfraction times startfraction 1 over x 1 endfraction startfraction 3 x over x 1 endfraction divided by startfraction 1 over x 1 endfraction startfraction x 1 over 1 endfraction divided by startfraction 3 x over x 1 endfraction startfraction x 1 over 3 x endfraction times startfraction x 1 over 1 endfraction

Answer 1

The equivalent expression of $\frac{3x}{x + 1} \div x + 1$ is $\frac{3x}{(x + 1)^2}$ or $\frac{3x}{x^2 +2x + 1}$

How to determine the equivalent expression?

The expression is given as:

$\frac{3x}{x + 1} \div x + 1$

Rewrite the expression as a product

$\frac{3x}{x + 1} \times \frac{1}{x + 1}$

Evaluate

$\frac{3x}{(x + 1)^2}$

Expand

$\frac{3x}{x^2 +2x + 1}$

Hence, the equivalent expression of $\frac{3x}{x + 1} \div x + 1$ is $\frac{3x}{(x + 1)^2}$ or $\frac{3x}{x^2 +2x + 1}$

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