Bananas1234
  • Bananas1234
Divide and simplify: (a-4)(a + 3)/a^2 - 2 divided by 2(a-4)/(a + 3)(a-1)
Mathematics
schrodinger
  • schrodinger
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Bananas1234
  • Bananas1234
Bananas1234
  • Bananas1234
jim_thompson5910
  • 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 \[\Large \frac{(a-4)(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2(a-4)}\]

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jim_thompson5910
  • jim_thompson5910
I'll let you simplify
Bananas1234
  • Bananas1234
im not sure i know how to simplify can you walk me through it? @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
well I can only see one pair of terms cancelling. Can you see it too?
Bananas1234
  • Bananas1234
the 2 (a + 3)
jim_thompson5910
  • jim_thompson5910
no, the "(a-4)" \[\Large \frac{(a-4)(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2(a-4)}\] \[\Large \frac{{\color{red}{(a-4)}}(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2{\color{red}{(a-4)}}}\] \[\Large \frac{{\color{red}{\cancel{(a-4)}}}(a+3)}{a^2-2} \times \frac{(a+3)(a-1)}{2{\color{red}{\cancel{(a-4)}}}}\] \[\Large \frac{a+3}{a^2-2} \times \frac{(a+3)(a-1)}{2}\]
Bananas1234
  • Bananas1234
i see
jim_thompson5910
  • jim_thompson5910
now multiply straight across
Bananas1234
  • Bananas1234
a+3^2/2a?
jim_thompson5910
  • jim_thompson5910
more like \[\Large \frac{a+3}{a^2-2} \times \frac{(a+3)(a-1)}{2}\] \[\Large \frac{(a+3)(a+3)(a-1)}{2(a^2-2)}\] \[\Large \frac{(a+3)^2(a-1)}{2(a^2-2)}\]
Bananas1234
  • Bananas1234
a+3^2/2?
jim_thompson5910
  • jim_thompson5910
you can't cancel anything else
Bananas1234
  • Bananas1234
so thats it? :)

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