Simplify (c^2-3c)/(c^2-25)*(c^2+4c-5)/(c^2-4c+3)

Factor ${\displaystyle c}$ out of ${\displaystyle c^2}$.

Factor ${\displaystyle c}$ out of ${\displaystyle -3c}$.

Factor ${\displaystyle c}$ out of ${\displaystyle c\cdot c+c\cdot -3}$.

Rewrite ${\displaystyle 25}$ as ${\displaystyle 5^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=c}$ and ${\displaystyle b=5}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -5}$ and whose sum is ${\displaystyle 4}$.

Write the factored form using these integers.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 3}$ and whose sum is ${\displaystyle -4}$.

Write the factored form using these integers.

Cancel the common factor of ${\displaystyle c-3}$.

Cancel the common factor of ${\displaystyle c+5}$.

Multiply ${\displaystyle \frac{c}{c-5}}$ by ${\displaystyle \frac{c-1}{c-1}}$.

Cancel the common factor of ${\displaystyle c-1}$.