i need help with rationals?

Question

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box.

 

 

a²+4a/(a³+3a²-4a)

 

Rational expression in lowest terms:

$\frac{a^2+4a}{a^3+3a^2-4a}$

 

Answer 1

Candice, if I am reading correctly, we can factor a out of the numerator.

 

a(a + 4)

 

We can also factor the denominator. We multiply a x c, 1 x -4 = -4. We need two factors of -4 that add up to equal b, 3.

 

-4 x 1 = -4, but - 4 + 1 = -3. Nope.

 

4 x -1 = -4 and 4 + (-1) = 3

 

a² + 3x - 4 = (a + 4)(a - 1)

 

Sooooo, we have...

 

a(a + 4)/(a + 4)(a - 1)

 

What cancels out? a + 4/a + 4 = 1, soooo...

 

a/(a - 1) is our answer.

 

Hope this helps!