Evaluate
\frac{y}{x}-\frac{5}{3}
Expand
\frac{y}{x}-\frac{5}{3}
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\frac{-\left(9x-8y\right)+4x-5y}{3x}
Since -\frac{9x-8y}{3x} and \frac{4x-5y}{3x} have the same denominator, add them by adding their numerators.
\frac{-9x+8y+4x-5y}{3x}
Do the multiplications in -\left(9x-8y\right)+4x-5y.
\frac{-5x+3y}{3x}
Combine like terms in -9x+8y+4x-5y.
\frac{-\left(9x-8y\right)+4x-5y}{3x}
Since -\frac{9x-8y}{3x} and \frac{4x-5y}{3x} have the same denominator, add them by adding their numerators.
\frac{-9x+8y+4x-5y}{3x}
Do the multiplications in -\left(9x-8y\right)+4x-5y.
\frac{-5x+3y}{3x}
Combine like terms in -9x+8y+4x-5y.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}