Evaluate
\frac{4x^{4}-16x^{3}-19x^{2}+85x+30}{2x-5}
Differentiate w.r.t. x
\frac{24x^{4}-144x^{3}+202x^{2}+190x-485}{\left(2x-5\right)^{2}}
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\frac{\left(2x^{3}-3x^{2}-17x\right)\left(2x-5\right)}{2x-5}+\frac{30}{2x-5}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{3}-3x^{2}-17x times \frac{2x-5}{2x-5}.
\frac{\left(2x^{3}-3x^{2}-17x\right)\left(2x-5\right)+30}{2x-5}
Since \frac{\left(2x^{3}-3x^{2}-17x\right)\left(2x-5\right)}{2x-5} and \frac{30}{2x-5} have the same denominator, add them by adding their numerators.
\frac{4x^{4}-10x^{3}-6x^{3}+15x^{2}-34x^{2}+85x+30}{2x-5}
Do the multiplications in \left(2x^{3}-3x^{2}-17x\right)\left(2x-5\right)+30.
\frac{4x^{4}-16x^{3}-19x^{2}+85x+30}{2x-5}
Combine like terms in 4x^{4}-10x^{3}-6x^{3}+15x^{2}-34x^{2}+85x+30.
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