QuestionCombine and simplify: $\frac{5 a-x}{6 a}-\frac{8 a+7 x}{2 a}+2$ into a single fraction.

Studdy Solution

STEP 1

Assumptions1. The variable $a$ is not equal to zero. . The variable $x$ can be any real number.

STEP 2

First, we need to find a common denominator for the fractions. The common denominator of $6a$ and $2a$ is $6a$ .

STEP 3

Now, we rewrite the fractions with the common denominator.
$\frac{5 a-x}{6 a}-\frac{3(8 a+7 x)}{6 a}+2$

STEP 4

Next, we subtract the fractions.
$\frac{ a-x-3(8 a+7 x)}{6 a}+2$

STEP 5

implify the numerator of the fraction.
$\frac{5 a-x-24 a-21 x}{ a}+2$

STEP 6

Combine like terms in the numerator.
$\frac{-19 a-22 x}{6 a}+2$

STEP 7

Now, we rewrite the fraction and the whole number with a common denominator.
$\frac{-19 a-22 x+12 a}{6 a}$

STEP 8

Combine like terms in the numerator.
$\frac{-7 a-22 x}{6 a}$ This is the simplified form of the given expression.

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