Multiply or divide as indicated
a. (5x+5)/6 multiplied by 3x/(x²+x)
5x + 5 3x
------ · ---------
6 x² + x
Factor 5x + 5 as 5(x + 1)
Factor x² + x as x(x + 1)
5(x + 1) 3x
-------- · ---------
6 x(x + 1)
Multiply numerators and denominators. Do not remove the
parentheses, though:
15x(x + 1)
------------
6x(x + 1)
15 and 6 can both be divided by 3
5
15x(x + 1)
------------
6x(x + 1)
2
We can also cancel the x's and the (x + 1)'s:
5 1
15x(x + 1)
------------
6x(x + 1)
2 1
Answer is simply:
5
---
2
========================================
b. (x²+x)/10 divided by (2x+4)/5
x² + x 2x + 4
------ ÷ ---------
10 5
To divide, invert the second and multiply
x² + x 5
------ · ---------
10 2x + 4
Factor x² + x as x(x + 1)
Factor 2x + 4 as 2(x + 2)
x(x + 1) 5
-------- · ---------
10 2(x + 2)
Multiply numerators and denominators. Do not remove the
parentheses, though:
5x(x + 1)
------------
20(x + 2)
Cancel the 5 into the 20
1
5x(x + 1)
------------
20(x + 2)
4
That's the only thing that will cancel, so the
answer is
x(x + 1)
------------
4(x + 2)
You can leave the answer like that, or, if you
want to, you can remove the parentheses and get
x² + x
--------
4x + 8
Edwin
