Split (3x² − 15x + 5)/(−3x) into separate fractions and simplify.

Step-by-step solution

1. 1

   Split term by term, keeping the negative denominator on each piece. The negative sign belongs to the divisor, so it acts on every term — this is where signs most often go astray:

   $\frac{3x^{2}}{-3x}-\frac{15x}{-3x}+\frac{5}{-3x}$

2. 2

   Simplify the first term.

   $\frac{3x^{2}}{-3x}=-x$

3. 3

   Simplify the second term. A negative divided by a negative is positive:

   $-\frac{15x}{-3x}=+5$

4. 4

   Simplify the third term. The $5$ has no $x$ to cancel, so it stays as a fraction:

   $\frac{5}{-3x}=-\frac{5}{3x}$

5. 5

   Reassemble.

   $\boxed{-x+5-\frac{5}{3x}}\qquad(x\neq 0)$

6. 6

   Check by multiplying back and numerically. $-3x\left(-x+5-\tfrac{5}{3x}\right)=3x^{2}-15x+5$ ✓. At $x=1$: the original is $\tfrac{3-15+5}{-3}=\tfrac{-7}{-3}=\tfrac73\approx 2.333$, and the answer gives $-1+5-\tfrac53=\tfrac73$ ✓.