Evaluate
\frac{8x^{2}+24x+\sqrt{2}}{2\left(x+3\right)}
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\frac{\frac{\sqrt{2}}{2}}{x+3}+4x
Get the value of \cos(45) from trigonometric values table.
\frac{\sqrt{2}}{2\left(x+3\right)}+4x
Express \frac{\frac{\sqrt{2}}{2}}{x+3} as a single fraction.
\frac{\sqrt{2}}{2\left(x+3\right)}+\frac{4x\times 2\left(x+3\right)}{2\left(x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4x times \frac{2\left(x+3\right)}{2\left(x+3\right)}.
\frac{\sqrt{2}+4x\times 2\left(x+3\right)}{2\left(x+3\right)}
Since \frac{\sqrt{2}}{2\left(x+3\right)} and \frac{4x\times 2\left(x+3\right)}{2\left(x+3\right)} have the same denominator, add them by adding their numerators.
\frac{\sqrt{2}+8x^{2}+24x}{2\left(x+3\right)}
Do the multiplications in \sqrt{2}+4x\times 2\left(x+3\right).
\frac{\sqrt{2}+8x^{2}+24x}{2x+6}
Expand 2\left(x+3\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Matrix
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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}