# Two algebra questions

After just taking the accuplacer exam for South University online I scored a 70 in Algebra.

I was not sure how to find the correct answers for two problems so I guessed. I’m hoping someone here can explain how to do them so I understand in the future.

``````

__ ______               __________
√     45            -      √     20

_____________________________

__________
√         5

``````

That should be the square root of 45 minus the square root of 20 over the square root of 5
And

``````

b  + b  [sup]2[/sup]
------------------------------------------------
b

``````

The general rule is that (a+b)/c = (a/c)+(b/c). Try that and see what you get.

The first question breaks down to:
(√45 - √20)/√5
=(√9√5 - √4√5)/√5
=(3√5 - 2√5)/√5
= (1√5)/√5
=1

The second is:
(b+b^2)/b

``````
b * (1 + b)
= -----------
b

``````

(the b’s ‘cancel out’ here, meaning that b/b = 1, so you are left with:
= 1 + b

Another way of looking at this last one, using **Valgard’s ** hint, is:
(b+b^2)/b

``````
b   b^2
= - + ---
b    b

1   b
= - + -
1   1

= 1 + b

``````
1. You could also multiply the entire thing by √5/√5 (i.e 1, so the overall value won’t change), converting to [√5 x (√45 - √20)] / (√5 x √5)

= (√5 x √45 - √5 x √20) / 5

= (√225 - √100) / 5

= (15-10) / 5

= 5 / 5

= 1

Ok so I got the first one wrong and the second one right.

However,
(b+b^2)/b = 1 + b
only if b is not equal to zero. If b = 0, the expression is undefined.