Question

Which choice is equivalent to the quotient shown here for acceptable values of x? sqrt25(x-1)÷sqrt5(x-1)^2

Answer 1

We have

`\frac{\sqrt[]{25(x-1)}}{\sqrt[]{5(x-1)^2}}`

we will use the next rules

`\sqrt[]{n\cdot m}=\sqrt[]{n}\sqrt[]{m}`
`\sqrt[]{m}=m^{(1)/(2)}`

with these in mind we can find the equivalent quotient.

`\frac{\sqrt[]{25(x-1)}}{\sqrt[]{5(x-1)^2}}=\frac{\sqrt[]{25}\sqrt[]{x-1}}{\sqrt[]{5}\sqrt[]{(x-1)^2}}=\frac{5(x-1)^{(1)/(2)}}{5^{(1)/(2)}(x-1)}`

then we will use

`(a^n)/(a^m)=a^(n-m)`

so we continue simplifying

`\frac{5(x-1)^{(1)/(2)}}{5^{(1)/(2)}(x-1)}=5^{1-(1)/(2)}(x-1)^{(1)/(2)-1}=5^{(1)/(2)}(x-1)^{-(1)/(2)}=\frac{\sqrt[]{5}}{\sqrt[]{x-1}}=\sqrt[]{(5)/(x-1)}`

the answer is B.