1. ## A few questions

I am brushing up on some math for an upcoming assessment test i have to take for post secondary. These questions are some that my teacher gave me, when i asked him what to expect for the assessment test (btw the last 2 are fractions, tried my best to make them look the part)

1. simplify (wasnt to sure where to go with this so i did what i knew)
= y-4[y-3(y-2)]5
= y-4[y^2 -2y-3y+6]5
= y-4[y^2 -5y+6]5
= y^3(?)-5y^2.... i know im wrong here

2.
_1_
1+1
a b
I think this is supposed to end up looking like this (im not sure of the process to get it however)
a+b
ab

3.Not sure how to do this one at all
___a__
a+a^2

2. Originally Posted by mode
I am brushing up on some math for an upcoming assessment test i have to take for post secondary. These questions are some that my teacher gave me, when i asked him what to expect for the assessment test (btw the last 2 are fractions, tried my best to make them look the part)

1. simplify (wasnt to sure where to go with this so i did what i knew)
= y-4[y-3(y-2)]5

= y - 20[y-3(y-2)]

= y - 20[y-3y+6]

= y - 20[-2y+6]

= y + 40y - 120

= 41y - 120

2.
_1_
1+1
a b
I think this is supposed to end up looking like this (im not sure of the process to get it however)
a+b
ab

multiply numerator and denominator by ab ... you should get ab/(b+a)

3.Not sure how to do this one at all
___a__
a+a^2

a/[a(1+a)] = 1/(1+a)
...

3. Originally Posted by mode
2.
_1_
1+1
a b
I think this is supposed to end up looking like this (im not sure of the process to get it however)
a+b
ab
\begin{aligned}
\frac{1}{\frac{1}{a} + \frac{1}{b}} &= \frac{1}{\frac{b}{ab} + \frac{a}{ab}} \\
&= \frac{1}{\frac{a + b}{ab}} \\
&= 1 \cdot \frac{ab}{a + b} \\
&= \frac{ab}{a + b}
\end{aligned}

3.Not sure how to do this one at all
___a__
a+a^2
\begin{aligned}
\frac{a}{a + a^2} &= \frac{a}{a(1 + a)} \\
&= \frac{1}{a + 1}
\end{aligned}

EDIT: Too slow!

4. thank you very much guys. Very helpful

5. Originally Posted by mode
I am brushing up on some math for an upcoming assessment test i have to take for post secondary. These questions are some that my teacher gave me, when i asked him what to expect for the assessment test (btw the last 2 are fractions, tried my best to make them look the part)

1. simplify (wasnt to sure where to go with this so i did what i knew)
= y-4[y-3(y-2)]5
skeeter is assuming this really is what you mean!

What you do below is (y- 4)[(y- 3)(y-2)]5. Do you see the difference?

= y-4[y^2 -2y-3y+6]5
= y-4[y^2 -5y+6]5
= y^3(?)-5y^2.... i know im wrong here

2.
_1_
1+1
a b
I think this is supposed to end up looking like this (im not sure of the process to get it however)
a+b
ab
$\frac{1}{\frac{1}{a}+ \frac{1}{b}}$
Multiply both numerator and denominator by ab:
$\frac{ab}{ab\frac{1}{a}+ ab\frac{1}{b}}= \frac{ab}{a+ b}$

3.Not sure how to do this one at all
___a__
a+a^2
$\frac{a}{a+ a^2}= \frac{a}{a(1+ a)}= \frac{1}{1+ a}$