Solve 5-39/5/4-34+3/6=9+frac{39/5}{4}-frac{6(frac{39}{5})-2}{16}

$$\frac { 5 - \frac { 39 } { 5 } } { 4 } - \frac { 34 + 3 } { 6 } = \frac { 9 + \frac { 39 } { 5 } } { 4 } - \frac { 6 ( \frac { 39 } { 5 } ) - 2 } { 16 }$$

Verify

Solution Steps

Multiply both sides of the equation by 48, the least common multiple of 4,6,16.

$$12\left(5-\frac{39}{5}\right)-8\left(34+3\right)=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Convert 5 to fraction \frac{25}{5}.

$$12\left(\frac{25}{5}-\frac{39}{5}\right)-8\left(34+3\right)=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Since \frac{25}{5} and \frac{39}{5} have the same denominator, subtract them by subtracting their numerators.

$$12\times \frac{25-39}{5}-8\left(34+3\right)=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Subtract 39 from 25 to get -14.

$$12\left(-\frac{14}{5}\right)-8\left(34+3\right)=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Express 12\left(-\frac{14}{5}\right) as a single fraction.

$$\frac{12\left(-14\right)}{5}-8\left(34+3\right)=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Multiply 12 and -14 to get -168.

$$\frac{-168}{5}-8\left(34+3\right)=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Fraction \frac{-168}{5} can be rewritten as -\frac{168}{5} by extracting the negative sign.

$$-\frac{168}{5}-8\left(34+3\right)=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Add 34 and 3 to get 37.

$$-\frac{168}{5}-8\times 37=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Multiply -8 and 37 to get -296.

$$-\frac{168}{5}-296=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Convert 296 to fraction \frac{1480}{5}.

$$-\frac{168}{5}-\frac{1480}{5}=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Since -\frac{168}{5} and \frac{1480}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-168-1480}{5}=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Subtract 1480 from -168 to get -1648.

$$-\frac{1648}{5}=12\left(9+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Convert 9 to fraction \frac{45}{5}.

$$-\frac{1648}{5}=12\left(\frac{45}{5}+\frac{39}{5}\right)-3\left(6\times \frac{39}{5}-2\right)$$

Since \frac{45}{5} and \frac{39}{5} have the same denominator, add them by adding their numerators.

$$-\frac{1648}{5}=12\times \frac{45+39}{5}-3\left(6\times \frac{39}{5}-2\right)$$

Add 45 and 39 to get 84.

$$-\frac{1648}{5}=12\times \frac{84}{5}-3\left(6\times \frac{39}{5}-2\right)$$

Express 12\times \frac{84}{5} as a single fraction.

$$-\frac{1648}{5}=\frac{12\times 84}{5}-3\left(6\times \frac{39}{5}-2\right)$$

Multiply 12 and 84 to get 1008.

$$-\frac{1648}{5}=\frac{1008}{5}-3\left(6\times \frac{39}{5}-2\right)$$

Express 6\times \frac{39}{5} as a single fraction.

$$-\frac{1648}{5}=\frac{1008}{5}-3\left(\frac{6\times 39}{5}-2\right)$$

Multiply 6 and 39 to get 234.

$$-\frac{1648}{5}=\frac{1008}{5}-3\left(\frac{234}{5}-2\right)$$

Convert 2 to fraction \frac{10}{5}.

$$-\frac{1648}{5}=\frac{1008}{5}-3\left(\frac{234}{5}-\frac{10}{5}\right)$$

Since \frac{234}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1648}{5}=\frac{1008}{5}-3\times \frac{234-10}{5}$$

Subtract 10 from 234 to get 224.

$$-\frac{1648}{5}=\frac{1008}{5}-3\times \frac{224}{5}$$

Express -3\times \frac{224}{5} as a single fraction.

$$-\frac{1648}{5}=\frac{1008}{5}+\frac{-3\times 224}{5}$$

Multiply -3 and 224 to get -672.

$$-\frac{1648}{5}=\frac{1008}{5}+\frac{-672}{5}$$

Fraction \frac{-672}{5} can be rewritten as -\frac{672}{5} by extracting the negative sign.

$$-\frac{1648}{5}=\frac{1008}{5}-\frac{672}{5}$$

Since \frac{1008}{5} and \frac{672}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1648}{5}=\frac{1008-672}{5}$$

Subtract 672 from 1008 to get 336.

$$-\frac{1648}{5}=\frac{336}{5}$$

Compare -\frac{1648}{5} and \frac{336}{5}.

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