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Algebra
5 problems similar to:
\frac { 2 } { x - y } + \frac { 5 } { y - x } + \frac { 3 } { x - y }
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\frac{2\left(-1\right)}{-x+y}+\frac{5}{-x+y}+\frac{3}{x-y}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-y and y-x is -x+y. Multiply \frac{2}{x-y} times \frac{-1}{-1}.
\frac{2\left(-1\right)+5}{-x+y}+\frac{3}{x-y}
Since \frac{2\left(-1\right)}{-x+y} and \frac{5}{-x+y} have the same denominator, add them by adding their numerators.
\frac{-2+5}{-x+y}+\frac{3}{x-y}
Do the multiplications in 2\left(-1\right)+5.
\frac{3}{-x+y}+\frac{3}{x-y}
Do the calculations in -2+5.
\frac{3}{-x+y}+\frac{3\left(-1\right)}{-x+y}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of -x+y and x-y is -x+y. Multiply \frac{3}{x-y} times \frac{-1}{-1}.
\frac{3+3\left(-1\right)}{-x+y}
Since \frac{3}{-x+y} and \frac{3\left(-1\right)}{-x+y} have the same denominator, add them by adding their numerators.
\frac{3-3}{-x+y}
Do the multiplications in 3+3\left(-1\right).
\frac{0}{-x+y}
Do the calculations in 3-3.
0
Zero divided by any non-zero term gives zero.
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}