## Bananas1234 one year ago Divide and simplify: (a-4)(a + 3)/a^2 - 2 divided by 2(a-4)/(a + 3)(a-1)

1. Bananas1234

@jim_thompson5910

2. Bananas1234

@robtobey

3. jim_thompson5910

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 $\Large \frac{(a-4)(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2(a-4)}$

4. jim_thompson5910

I'll let you simplify

5. Bananas1234

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

6. jim_thompson5910

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

7. Bananas1234

the 2 (a + 3)

8. jim_thompson5910

no, the "(a-4)" $\Large \frac{(a-4)(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2(a-4)}$ $\Large \frac{{\color{red}{(a-4)}}(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2{\color{red}{(a-4)}}}$ $\Large \frac{{\color{red}{\cancel{(a-4)}}}(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2{\color{red}{\cancel{(a-4)}}}}$ $\Large \frac{a+3}{a^2-2} \times \frac{(a+3)(a-1)}{2}$

9. Bananas1234

i see

10. jim_thompson5910

now multiply straight across

11. Bananas1234

a+3^2/2a?

12. jim_thompson5910

more like $\Large \frac{a+3}{a^2-2} \times \frac{(a+3)(a-1)}{2}$ $\Large \frac{(a+3)(a+3)(a-1)}{2(a^2-2)}$ $\Large \frac{(a+3)^2(a-1)}{2(a^2-2)}$

13. Bananas1234

a+3^2/2?

14. jim_thompson5910

you can't cancel anything else

15. Bananas1234

so thats it? :)

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