Solve 3(12/34)+-38/13+3(4/3)=0

$$3 ( \frac { 12 } { 34 } ) + \frac { - 38 } { 13 } + 3 ( \frac { 4 } { 3 } ) = 0$$

Verify

Solution Steps

Reduce the fraction \frac{12}{34} to lowest terms by extracting and canceling out 2.

$$3\times \frac{6}{17}+\frac{-38}{13}+3\times \frac{4}{3}=0$$

Express 3\times \frac{6}{17} as a single fraction.

$$\frac{3\times 6}{17}+\frac{-38}{13}+3\times \frac{4}{3}=0$$

Multiply 3 and 6 to get 18.

$$\frac{18}{17}+\frac{-38}{13}+3\times \frac{4}{3}=0$$

Fraction \frac{-38}{13} can be rewritten as -\frac{38}{13} by extracting the negative sign.

$$\frac{18}{17}-\frac{38}{13}+3\times \frac{4}{3}=0$$

Least common multiple of 17 and 13 is 221. Convert \frac{18}{17} and \frac{38}{13} to fractions with denominator 221.

$$\frac{234}{221}-\frac{646}{221}+3\times \frac{4}{3}=0$$

Since \frac{234}{221} and \frac{646}{221} have the same denominator, subtract them by subtracting their numerators.

$$\frac{234-646}{221}+3\times \frac{4}{3}=0$$

Subtract 646 from 234 to get -412.

$$-\frac{412}{221}+3\times \frac{4}{3}=0$$

Cancel out 3 and 3.

$$-\frac{412}{221}+4=0$$

Convert 4 to fraction \frac{884}{221}.

$$-\frac{412}{221}+\frac{884}{221}=0$$

Since -\frac{412}{221} and \frac{884}{221} have the same denominator, add them by adding their numerators.

$$\frac{-412+884}{221}=0$$

Add -412 and 884 to get 472.

$$\frac{472}{221}=0$$

Compare \frac{472}{221} and 0.

$$\text{false}$$