Question

determine the quotient of each expression. describe any restriction(s) for the variables and simplify the answer when possible.

1. \\(\frac{3c^2}{5ab} \div \frac{9}{2a}\\)
2. \\(\frac{4x^2y}{z^4} \div \frac{2x}{z} \div \frac{1}{2z}\\)
3. \\(\frac{26ab}{4a} \div \frac{39a^4b^3}{12b^4}\\)
4. \\(\frac{x^2 + 4x + 3}{2x^2 - 11x + 5} \div \frac{x^2 + 3x}{2x - 1}\\)
5. \\(\frac{x^2 - 121}{x^2 + x - 20} \div \frac{x^2 - 10x - 11}{x^2 - 25}\\)
6. \\(\frac{x^2 + 4x + 3}{2x^2 - 11x + 5} \div \frac{x^2 + 3x}{2x - 1}\\)

Explanation:

Answer:

1. $\frac{2c^2}{15b}$, restrictions: $a

eq 0$, $b
eq 0$

1. $\frac{4x y}{z^2}$, restrictions: $x

eq 0$, $z
eq 0$

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

eq 0$, $b
eq 0$

1. $\frac{x+1}{x(x-5)}$, restrictions: $x

eq 0$, $x
eq 5$, $x
eq \frac{1}{2}$, $x
eq -3$

1. $\frac{(x+11)(x-5)}{(x+5)(x-11)}$, restrictions: $x

eq -5$, $x
eq 4$, $x
eq 11$, $x
eq -1$

1. $\frac{x+1}{x(x-5)}$, restrictions: $x

eq 0$, $x
eq 5$, $x
eq \frac{1}{2}$, $x
eq -3$