Evaluate
\frac{5x+y}{x^{2}+y^{2}}
Expand
\frac{5x+y}{x^{2}+y^{2}}
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\frac{\left(5x+y\right)\left(2x-3y\right)}{\left(4x+y\right)\left(2x-3y\right)}\times \frac{2y+8x}{2x^{2}+2y^{2}}
Factor the expressions that are not already factored in \frac{10x^{2}-13xy-3y^{2}}{8x^{2}-10xy-3y^{2}}.
\frac{5x+y}{4x+y}\times \frac{2y+8x}{2x^{2}+2y^{2}}
Cancel out 2x-3y in both numerator and denominator.
\frac{5x+y}{4x+y}\times \frac{2\left(4x+y\right)}{2\left(x^{2}+y^{2}\right)}
Factor the expressions that are not already factored in \frac{2y+8x}{2x^{2}+2y^{2}}.
\frac{5x+y}{4x+y}\times \frac{4x+y}{x^{2}+y^{2}}
Cancel out 2 in both numerator and denominator.
\frac{\left(5x+y\right)\left(4x+y\right)}{\left(4x+y\right)\left(x^{2}+y^{2}\right)}
Multiply \frac{5x+y}{4x+y} times \frac{4x+y}{x^{2}+y^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{5x+y}{x^{2}+y^{2}}
Cancel out 4x+y in both numerator and denominator.
\frac{\left(5x+y\right)\left(2x-3y\right)}{\left(4x+y\right)\left(2x-3y\right)}\times \frac{2y+8x}{2x^{2}+2y^{2}}
Factor the expressions that are not already factored in \frac{10x^{2}-13xy-3y^{2}}{8x^{2}-10xy-3y^{2}}.
\frac{5x+y}{4x+y}\times \frac{2y+8x}{2x^{2}+2y^{2}}
Cancel out 2x-3y in both numerator and denominator.
\frac{5x+y}{4x+y}\times \frac{2\left(4x+y\right)}{2\left(x^{2}+y^{2}\right)}
Factor the expressions that are not already factored in \frac{2y+8x}{2x^{2}+2y^{2}}.
\frac{5x+y}{4x+y}\times \frac{4x+y}{x^{2}+y^{2}}
Cancel out 2 in both numerator and denominator.
\frac{\left(5x+y\right)\left(4x+y\right)}{\left(4x+y\right)\left(x^{2}+y^{2}\right)}
Multiply \frac{5x+y}{4x+y} times \frac{4x+y}{x^{2}+y^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{5x+y}{x^{2}+y^{2}}
Cancel out 4x+y in both numerator and denominator.
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}