# Two algebra questions

**URL:** <https://boards.straightdope.com/t/two-algebra-questions/384728>\
**Category:** Factual Questions\
**Created:** [December 19, 2006, 2:29am UTC](https://boards.straightdope.com/t/two-algebra-questions/384728 "2006-12-19T02:29:28Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![MannyL](https://avatars.discourse-cdn.com/v4/letter/m/ba8739/32.png) [@MannyL](https://boards.straightdope.com/u/MannyL)\
**Post date:** [December 19, 2006, 2:29am UTC](https://boards.straightdope.com/t/two-algebra-questions/384728/1 "2006-12-19T02:29:28Z")

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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.

```auto

 
  ________  __________           
√ 45 - √ 20            

_____________________________

             __________
           √ 5

```

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

```auto

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

```

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**Author:** ![Valgard](https://avatars.discourse-cdn.com/v4/letter/v/7feea3/32.png) [@Valgard](https://boards.straightdope.com/u/Valgard)\
**Post date:** [December 19, 2006, 2:35am UTC](https://boards.straightdope.com/t/two-algebra-questions/384728/2 "2006-12-19T02:35:40Z")

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

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**Author:** ![ArmenE](https://avatars.discourse-cdn.com/v4/letter/a/e9bcb4/32.png) [@ArmenE](https://boards.straightdope.com/u/ArmenE)\
**Post date:** [December 19, 2006, 3:20am UTC](https://boards.straightdope.com/t/two-algebra-questions/384728/3 "2006-12-19T03:20:17Z")

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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

```auto

  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

```auto

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

  1 b
= - + -
  1 1

= 1 + b

```

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<div class="post-metadata">

**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\
**Post date:** [December 19, 2006, 3:32am UTC](https://boards.straightdope.com/t/two-algebra-questions/384728/4 "2006-12-19T03:32:07Z")

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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

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**Author:** ![MannyL](https://avatars.discourse-cdn.com/v4/letter/m/ba8739/32.png) [@MannyL](https://boards.straightdope.com/u/MannyL)\
**Post date:** [December 19, 2006, 4:49am UTC](https://boards.straightdope.com/t/two-algebra-questions/384728/5 "2006-12-19T04:49:51Z")

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

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**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\
**Post date:** [December 19, 2006, 12:23pm UTC](https://boards.straightdope.com/t/two-algebra-questions/384728/6 "2006-12-19T12:23:30Z")

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