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\frac{\left(2x^{4}+5x^{3}+5x^{2}+10x+2\right)x}{x}+\frac{8}{x}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{4}+5x^{3}+5x^{2}+10x+2 times \frac{x}{x}.
\frac{\left(2x^{4}+5x^{3}+5x^{2}+10x+2\right)x+8}{x}
Since \frac{\left(2x^{4}+5x^{3}+5x^{2}+10x+2\right)x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.
\frac{2x^{5}+5x^{4}+5x^{3}+10x^{2}+2x+8}{x}
Do the multiplications in \left(2x^{4}+5x^{3}+5x^{2}+10x+2\right)x+8.