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5\left(4\times \frac{17}{10}-1\right)-12=5\times 2\times \frac{17}{10}
Multiply both sides of the equation by 15, the least common multiple of 3,5.
5\left(\frac{4\times 17}{10}-1\right)-12=5\times 2\times \frac{17}{10}
Express 4\times \frac{17}{10} as a single fraction.
5\left(\frac{68}{10}-1\right)-12=5\times 2\times \frac{17}{10}
Multiply 4 and 17 to get 68.
5\left(\frac{34}{5}-1\right)-12=5\times 2\times \frac{17}{10}
Reduce the fraction \frac{68}{10} to lowest terms by extracting and canceling out 2.
5\left(\frac{34}{5}-\frac{5}{5}\right)-12=5\times 2\times \frac{17}{10}
Convert 1 to fraction \frac{5}{5}.
5\times \frac{34-5}{5}-12=5\times 2\times \frac{17}{10}
Since \frac{34}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.
5\times \frac{29}{5}-12=5\times 2\times \frac{17}{10}
Subtract 5 from 34 to get 29.
29-12=5\times 2\times \frac{17}{10}
Cancel out 5 and 5.
17=5\times 2\times \frac{17}{10}
Subtract 12 from 29 to get 17.
17=10\times \frac{17}{10}
Multiply 5 and 2 to get 10.
17=17
Cancel out 10 and 10.
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Compare 17 and 17.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}