Evaluate
\frac{6y\left(y+1\right)}{x\left(x+1\right)}
Expand
\frac{6\left(y^{2}+y\right)}{x\left(x+1\right)}
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\frac{8xy\times 15\left(y+1\right)}{5\left(x+1\right)\times 4x^{2}}
Divide \frac{8xy}{5\left(x+1\right)} by \frac{4x^{2}}{15\left(y+1\right)} by multiplying \frac{8xy}{5\left(x+1\right)} by the reciprocal of \frac{4x^{2}}{15\left(y+1\right)}.
\frac{2\times 3y\left(y+1\right)}{x\left(x+1\right)}
Cancel out 4\times 5x in both numerator and denominator.
\frac{6y\left(y+1\right)}{x\left(x+1\right)}
Multiply 2 and 3 to get 6.
\frac{6y^{2}+6y}{x\left(x+1\right)}
Use the distributive property to multiply 6y by y+1.
\frac{6y^{2}+6y}{x^{2}+x}
Use the distributive property to multiply x by x+1.
\frac{8xy\times 15\left(y+1\right)}{5\left(x+1\right)\times 4x^{2}}
Divide \frac{8xy}{5\left(x+1\right)} by \frac{4x^{2}}{15\left(y+1\right)} by multiplying \frac{8xy}{5\left(x+1\right)} by the reciprocal of \frac{4x^{2}}{15\left(y+1\right)}.
\frac{2\times 3y\left(y+1\right)}{x\left(x+1\right)}
Cancel out 4\times 5x in both numerator and denominator.
\frac{6y\left(y+1\right)}{x\left(x+1\right)}
Multiply 2 and 3 to get 6.
\frac{6y^{2}+6y}{x\left(x+1\right)}
Use the distributive property to multiply 6y by y+1.
\frac{6y^{2}+6y}{x^{2}+x}
Use the distributive property to multiply x by x+1.
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}