Factor and simplify. Express the answer as a fraction without negative exponents. x(x - 1)^{-(1)/(2)}+2(x - 1)^{(1)/(2) } Answers with no explanations will be reported. Random an…

Question

Factor and simplify. Express the answer as a fraction without negative exponents.


`x(x - 1)^{-(1)/(2)}+2(x - 1)^{(1)/(2) }`


Answers with no explanations will be reported. Random answers will be reported.

Answer 1

Explanation:

We have to simplify:

`x(x - 1)^{-(1)/(2)}+2(x - 1)^{(1)/(2) }`

`= \large{(x)/( √(x - 1) ) + 2 √(x - 1)}`

Taking a common denominator,

`=\large{(x + 2 √(x - 1) * √(x - 1) )/( √(x - 1) )}`

`=\large{(x + 2(x - 1))/( √(x - 1) )}`

Opening the parentheses in numerator,

`=\large{ (x + 2x - 2)/( √(x - 1)) }`

`=\large{(3x - 2)/( √(x - 1) )}`

Now multiplying
`√(x - 1)` in both numerator and denominator,

`=\large{(3x - 2 * √(x - 1) )/( √(x - 1) * √(x - 1) )}`

`=\large{(3x - 2 * √(x - 1) )/(x - 1) }`

`= \boxed{\frac{3x - 2(x - 1) {}^{ (1)/(2) } }{x - 1} }`