Write as a single fraction in its simplest form (2x-1/3)

Ответ:

sbednarek

13.02.2022

Mathematics

We want to write the given expression as a single fraction. We will get the fraction:

$\frac{6*x^2 - 4*x - 6}{3*x}$

Rewriting the expression.

So we start with the expression:

$(2*x - \frac{1}{3}) - (\frac{2}{x} + 1)$

First, let's rewrite each of these parenthesis as fractions, we need to have the same denominator in all the terms, then in the first one we can multiply and divide by 3 (and in the second one we can do the same but with x) so we get:

$(\frac{3}{3} *2*x - \frac{1}{3}) - (\frac{2}{x} + 1*\frac{x}{x} )\\\\(\frac{6*x}{3} - \frac{1}{3}) - (\frac{2}{x} + \frac{x}{x} )\\\\\frac{6*x - 1}{3} - \frac{2 + x}{x}$

Now we must multiply and divide the left term by x, and the right term by 3, so we get:

$\frac{x}{x} \frac{6*x - 1}{3} - \frac{2 + x}{x}*\frac{3}{3} \\\\\frac{6*x^2 - x}{3*x} - \frac{6 + 3x}{3*x} = \frac{6*x^2 - x - 3x - 6}{3*x}\\\\\frac{6*x^2 - 4*x - 6}{3*x}$