Simplifying Algebraic Expressions

Question

(3x-8)/((4x-3)^(4/3) (x+5)^(1/2))

Answer 1

This is already simplified. Am I to figure for "x"? If so all I can do is guess then multiply.

Answer 2

Assuming you want to rationalize the denominator (using proper nomenclature is very helpful)

The denominator must be multiplied thus

(4x - 3)^4/3(4x - 3)^2/3(x + 5)^1/2(x + 5)^1/2

resulting in

(4x - 3)²(x + 5)

The same multiplication must be done to the numerator

(3x - 8)(4x - 3)^2/3(x + 5)^1/2

That can be written

(3x - 8)(4x - 3)²(4x - 3)^1/3(x + 5)^1/2

The (4x - 3)² in the numerator and denominator can be reduced, leaving

(3x - 8)(4x - 3)^1/3(x + 5)^1/2 / (x + 5)