Simplify the Rational Expression: (2x-1)/(16x²-8x) Step-by-Step

Question

Simplify the following expression:

$\frac{2x-1}{16x^2-8x}$

Video Solution

Solution Steps

00:00 Simply

00:07 Let's break down 16 into factors 2 and 8

00:10 Let's break down the exponent into multiplications

00:17 Let's mark the common factors

00:35 Let's take out the common factors from the parentheses

00:49 Let's reduce what we can

00:55 And this is the solution to the question

Step-by-Step Solution

Let's simplify the given expression:

$\frac{2x-1}{16x^2-8x}$ Remember that we can reduce complete expressions only when both the numerator and denominator are completely factored into multiplication expressions,

For this, we'll use factorization, identify that in the denominator we can factor out a common term, do this, then reduce the expressions possible in the fraction that we obtained:

$\frac{2x-1}{16x^2-8x} \\ \frac{2x-1}{8x(2x-1)} \\ \downarrow\\ \boxed{\frac{1}{8x}}$ Therefore, the correct answer is answer C.

Answer

$\frac{1}{8x}$

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