Question

multiply. factor first, check for gcfs! state any restrictions. then simplify if possible.

1. $\frac{4}{5x} cdot \frac{3}{2x^2}$

restrictions: $x \
eq$ _______

1. $\frac{3x+6}{4x^2} cdot \frac{16x}{x+2}$

restrictions: $x \
eq$ _______

Explanation:

Step1: Multiply numerators/denominators (Q4)

$\frac{4}{5x} \cdot \frac{3}{2x^2} = \frac{4 \cdot 3}{5x \cdot 2x^2} = \frac{12}{10x^3}$

Step2: Simplify the fraction (Q4)

$\frac{12}{10x^3} = \frac{6}{5x}$

Step3: Identify restrictions (Q4)

Denominators can't be 0: $5x
eq 0$ and $2x^2
eq 0 \implies x
eq 0$

Step4: Factor numerator (Q5)

$3x+6 = 3(x+2)$

Step5: Multiply fractions (Q5)

$\frac{3(x+2)}{4x^2} \cdot \frac{16x}{x+2} = \frac{3(x+2) \cdot 16x}{4x^2 \cdot (x+2)}$

Step6: Cancel common factors (Q5)

$\frac{3 \cdot 16x}{4x^2} = \frac{48x}{4x^2} = \frac{12}{x}$

Step7: Identify restrictions (Q5)

Denominators can't be 0: $4x^2
eq 0$, $x+2
eq 0 \implies x
eq 0, -2$

Answer:

1. $\boldsymbol{\frac{6}{5x}}$; Restriction: $x

eq 0$

1. $\boldsymbol{\frac{12}{x}}$; Restriction: $x

eq 0, -2$