# How do you simplify \frac { 10h ^ { 2} - 17h + 3} { 3h - 3} \cdot \frac { h - 1} { 10h ^ { 2} - 17h + 3}?

Oct 11, 2017

$\frac{10 {h}^{2} - 17 h + 3}{3 h - 3} \cdot \frac{h - 1}{10 {h}^{2} - 17 h + 3} = \frac{1}{3}$

#### Explanation:

$\frac{10 {h}^{2} - 17 h + 3}{3 h - 3} \cdot \frac{h - 1}{10 {h}^{2} - 17 h + 3} = \frac{\cancel{\left(10 {h}^{2} - 17 h + 3\right)} \cancel{\left(h - 1\right)}}{3 \cancel{\left(h - 1\right)} \cancel{\left(10 {h}^{2} - 17 h + 3\right)}} = \frac{1}{3}$

Oct 11, 2017

$\frac{1}{3}$

#### Explanation:

...when multiplying terms like this, where you have numerators and denominators, any factor appearing in both a numerator and denominator can be cancelled out.

So right away, your polynomial $10 {h}^{2} - 17 h + 3$, which appears in the numerator of one term and denominator of the other, cancels out. This leaves:

$\frac{h - 1}{3 h - 3}$

...and you can factor out a 3 from the denominator:

$\frac{h - 1}{3 \left(h - 1\right)}$

...and once again you have a term $\left(h - 1\right)$ appearing in both numerator & denominator, which cancels out, leaving

$\frac{1}{3}$

GOOD LUCK