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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).