1. cancelling in fractions

I am doing this problem a+3 / a - 5 x 2a - 10 / 3a + 9 the answer given is 2/3 but as there are 3 a's in the numerator line and 4 a's in the denominator line how do these cancell out?

2. Originally Posted by tanch
I am doing this problem a+3 / a - 5 x 2a - 10 / 3a + 9 the answer given is 2/3 but as there are 3 a's in the numerator line and 4 a's in the denominator line how do these cancell out?
ok, you need to be more clear as to what you mean. if you can't use latex, type fractions like this:

(numerator)/(denominator)

example, type (2x + 5)/(x + 9) to mean $\frac {2x + 5}{x + 9}$

i think you mean $\frac {a + 3}{a - 5} \times \frac {2a - 10}{3a + 9}$ but i am not sure. that is certainly not what you typed, but it is probably what you meant

3. Firstly, please use parantheses when you write a problem.

I assume you are asking for this:

$\frac{a+3}{a-5}\cdot \frac{2a - 10}{3a + 9}$

Factorize 2a-10 and 3a+9.

$\frac{\not a+\not 3}{\not a-\not 5}\cdot \frac{2 (\not a- \not 5)}{3 ( \not a+\not 3)}$

$\frac{2}{3}$

4. Originally Posted by tanch
I am doing this problem a+3 / a - 5 x 2a - 10 / 3a + 9 the answer given is 2/3 but as there are 3 a's in the numerator line and 4 a's in the denominator line how do these cancell out?
"Cancel"? What is that? Never do that.

$\frac{a+3}{a-5}*\frac{2a-10}{3a+9} =$

$\frac{a+3}{a-5}*\frac{2(a-5)}{3(a+3)} =$ -- That's right, the Distributive Property of Multiplication over Addition

$\frac{a+3}{a-5}*\frac{2}{3}*\frac{a-5}{a+3} =$ -- What's that? Multiplication?

$\frac{2}{3}*\frac{a+3}{a-5}*\frac{a-5}{a+3} =$ -- Now we see the Commutative Property of Multiplication.

$\frac{2}{3}*\frac{a+3}{a+3}*\frac{a-5}{a-5} =$ -- Same thing, but only in the denominators.

$\frac{2}{3}*1*1 = \frac{2}{3}$ -- At last, an Identity Definition and Identity Property

There is no "cancelling" going on in there. "Cancelling" is bad. Properties of mathematics will solve math problems. There is a reason why you studied those properties. I dare you to show me a text book that describes the "Property of Cancelling".

Special Note: This is good only for $a \neq 5$ and $a \neq -3$. You tell me why.

5. Thank you
That explanation makes it clear, The answer will not work if a = 5 beacause the term a - 5 = 0 yes?

6. Will you ever use "Cancel" again?

Right. Even though it does not appear in the final statement, 2/3, it was in the ORIGINAL problem statement and must be considered. Same for -3.

Good work.

7. No more cancelling! I think my problem was looking for shortcuts, but short cuts make long delays! thanks again