Answer
$ 2x^2-4x+1-\frac{10}{5x-3}$.
Work Step by Step
The given expression is
$(10x^3-26x^2+17x-13)\div(5x-3)$
$\begin{matrix}
& 2x^2 & -4x&+1 & & \leftarrow &Quotient\\
&-- &-- &--& \\
5x-3) &10x^3&-26x^2&+17x&-13 & \\
& 10x^3&-6x^2 & & & \leftarrow &2x^2(5x-3) \\
& -- & -- & & & \leftarrow &subtract \\
& 0 & -20x^2 &+17x& & \\
& & -20x^2 & +12x & & \leftarrow & -4x(5x-3) \\
& & -- & -- && \leftarrow & subtract \\
& & 0&5x &-13&\\
& & &5x &-3&\leftarrow & +1(5x-3)\\
& & & -- & -- & \leftarrow & subtract \\
& & &0 &-10&\leftarrow & Remainder
\end{matrix}$
The answer is
$\Rightarrow Quotient + \frac{Remainder}{Divisor}$
$\Rightarrow 2x^2-4x+1-\frac{10}{5x-3}$.
