Evaluate
\frac{\left(ac\right)^{2}}{2\left(a^{2}-c^{2}\right)}
Expand
-\frac{\left(ac\right)^{2}}{2\left(c^{2}-a^{2}\right)}
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\frac{a^{2}c^{2}}{\left(a+c\right)^{2}}\times \frac{3\left(a+c\right)}{6\left(a-c\right)}
Factor the expressions that are not already factored in \frac{3a+3c}{6a-6c}.
\frac{a^{2}c^{2}}{\left(a+c\right)^{2}}\times \frac{a+c}{2\left(a-c\right)}
Cancel out 3 in both numerator and denominator.
\frac{a^{2}c^{2}\left(a+c\right)}{\left(a+c\right)^{2}\times 2\left(a-c\right)}
Multiply \frac{a^{2}c^{2}}{\left(a+c\right)^{2}} times \frac{a+c}{2\left(a-c\right)} by multiplying numerator times numerator and denominator times denominator.
\frac{a^{2}c^{2}}{2\left(a+c\right)\left(a-c\right)}
Cancel out a+c in both numerator and denominator.
\frac{a^{2}c^{2}}{\left(2a+2c\right)\left(a-c\right)}
Use the distributive property to multiply 2 by a+c.
\frac{a^{2}c^{2}}{2a^{2}-2c^{2}}
Use the distributive property to multiply 2a+2c by a-c and combine like terms.
\frac{a^{2}c^{2}}{\left(a+c\right)^{2}}\times \frac{3\left(a+c\right)}{6\left(a-c\right)}
Factor the expressions that are not already factored in \frac{3a+3c}{6a-6c}.
\frac{a^{2}c^{2}}{\left(a+c\right)^{2}}\times \frac{a+c}{2\left(a-c\right)}
Cancel out 3 in both numerator and denominator.
\frac{a^{2}c^{2}\left(a+c\right)}{\left(a+c\right)^{2}\times 2\left(a-c\right)}
Multiply \frac{a^{2}c^{2}}{\left(a+c\right)^{2}} times \frac{a+c}{2\left(a-c\right)} by multiplying numerator times numerator and denominator times denominator.
\frac{a^{2}c^{2}}{2\left(a+c\right)\left(a-c\right)}
Cancel out a+c in both numerator and denominator.
\frac{a^{2}c^{2}}{\left(2a+2c\right)\left(a-c\right)}
Use the distributive property to multiply 2 by a+c.
\frac{a^{2}c^{2}}{2a^{2}-2c^{2}}
Use the distributive property to multiply 2a+2c by a-c and combine like terms.
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}