How do you combine $\frac{x - 3}{30 x + 5} - \frac{2}{18 x + 3}$ $(x-3)/ (30x+5) - 2/ (18x+3)$ ?

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How do you combine $\frac{x - 3}{30 x + 5} - \frac{2}{18 x + 3}$ $(x-3)/ (30x+5) - 2/ (18x+3)$ ?

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Answer 1 · 2015-05-19T16:32:19

First, let's have a look at the two terms of our sum:

$\frac{x - 3}{30 x + 5}$ $(x - 3) / (30 x + 5)$ = $\frac{x - 3}{5 (6 x + 1)}$ $(x - 3) / (5(6 x + 1))$

$\frac{2}{18 x + 3}$ $2 / (18 x + 3)$ = $\frac{2}{3 (6 x + 1)}$ $2 / (3(6 x + 1))$

Notice that the least common denominator is $5 \cdot 3 \cdot (6 x + 1) = 15 (6 x + 1)$ $5 * 3 * (6 x + 1) = 15(6 x + 1)$ . This means that we have to multiply the first term by $3$ $3$ and the second term by $5$ $5$ .

This gives: $\frac{3 (x - 3) - 2 \cdot 5}{15 (6 x + 1)}$ $(3(x - 3) - 2 * 5) / (15(6 x + 1))$ = $\frac{3 x - 19}{15 (6 x + 1)}$ $(3 x - 19) / (15(6 x + 1))$ = $\frac{3 x - 19}{90 x + 15}$ $(3 x - 19) / (90 x + 15)$

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How do you combine $\frac{x - 3}{30 x + 5} - \frac{2}{18 x + 3}$ $(x-3)/ (30x+5) - 2/ (18x+3)$ ?

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