Question

Divide and simplify:
(a-4)(a + 3)/a^2 - 2 divided by 2(a-4)/(a + 3)(a-1)

Answer 1

@jim_thompson5910

Answer 2

@robtobey

Answer 3

When you divide two fractions, you will flip the second fraction and multiply

Example: 1/2 divided by 3/4 = 1/2 times 4/3

So in this case, it means
\[\Large \frac{(a-4)(a+3)}{a^2-2} \div \frac{2(a-4)}{(a+3)(a-1)}\]
turns into
\[\Large \frac{(a-4)(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2(a-4)}\]

Answer 4

I'll let you simplify

Answer 5

im not sure i know how to simplify can you walk me through it? @jim_thompson5910

Answer 6

well I can only see one pair of terms cancelling. Can you see it too?

Answer 7

the 2 (a + 3)

Answer 8

no, the "(a-4)"

\[\Large \frac{(a-4)(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2(a-4)}\]
\[\Large \frac{{\color{red}{(a-4)}}(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2{\color{red}{(a-4)}}}\]
\[\Large \frac{{\color{red}{\cancel{(a-4)}}}(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2{\color{red}{\cancel{(a-4)}}}}\]
\[\Large \frac{a+3}{a^2-2} \times \frac{(a+3)(a-1)}{2}\]

Answer 9

i see

Answer 10

now multiply straight across

Answer 11

a+3^2/2a?

Answer 12

more like

\[\Large \frac{a+3}{a^2-2} \times \frac{(a+3)(a-1)}{2}\]
\[\Large \frac{(a+3)(a+3)(a-1)}{2(a^2-2)}\]
\[\Large \frac{(a+3)^2(a-1)}{2(a^2-2)}\]

Answer 13

a+3^2/2?

Answer 14

you can't cancel anything else

Answer 15

so thats it? :)