Question

Simplify the following rational expression to determine if thegiven simplification is correct. If it is correct, select TRUE. If it isnot correct, select FALSE.6x48x556x47

Answer 1

The question asks us to confirm the simplification of the expression:

$-\frac{48x^5}{56x^4}$

Step 1: Factor the numbers

$\begin{gathered} 48=8\times6 \\ 56=8\times7 \end{gathered}$

Therefore, the expression becomes:

$-\frac{48x^5}{56x^4}=-\frac{8\times6x^5}{8\times7x^4}$

Step 2: Cancel out the common terms from the expression

$-\frac{8\times6x^5}{8\times7x^4}=-\frac{6x^5}{7x^4}$

Step 3: Apply the rule of exponents

$\frac{x^n}{x^n}=x^{m-n}$

Therefore, we have:

$-\frac{6x^5}{7x^4}=\frac{6}{7}x^{5-4}=-\frac{6x}{7}$

CONCLUSION

The expression simplifies to give:

$-\frac{48x^5}{56x^4}=-\frac{6x}{7}$

The answer is TRUE.