Question

date: 1/30/2026
multiply each expression. describe any restriction(s) for the variables and simplify the
answer when possible.

1. \\(\frac{3mn^2}{10} \cdot \frac{m^2}{8n} \cdot \frac{20}{3m^2}\\)
2. \\(\frac{2ab^2}{bc^3} \cdot \frac{15c^3}{10a}\\)
3. \\(\frac{5x^2}{x + 4} \cdot \frac{3x^2 + 12x}{7x - 7} \cdot \frac{x^2 - 2x + 1}{3}\\)
4. \\(\frac{x^2 + 2x - 3}{x^2} \cdot \frac{x^3 + x^2}{x + 3}\\)
5. \\(\frac{1}{2x^2 + 3x - 2} \cdot \frac{x^2 - 2x - 8}{x - 4}\\)
6. \\(\frac{x + 3}{x - 5} \cdot \frac{x^2 - 25}{x^2 + 6x + 9}\\)

Explanation:

Answer:

1. $\frac{m^3}{4n}$, $m

eq 0$, $n
eq 0$

1. $\frac{3b^2}{2c^3}$, $a

eq 0$, $c
eq 0$

1. $\frac{5x^3(x-1)}{7}$, $x

eq -4$, $x
eq 1$

1. $x^2(x-1)$, $x

eq -3$, $x
eq 0$

1. $\frac{1}{2x-1}$, $x

eq -2$, $x
eq \frac{1}{2}$, $x
eq 4$

1. $\frac{x+5}{x+3}$, $x

eq 5$, $x
eq -3$