Just a few question?

Question

Find all numbers for wich the tational expression is undefined.

7 / 3y + 5

= 0?

t^2 + 5t / t^2 + 3t - 10 dived by t / t + 2

= t + 2 / t -2

simplify by removing factors of 1.

p^2 - 25 / p^2 - 10 p + 25

= p + 5 / p - 5

This one I am confused on. I do not know where to start at.

1 / v = 9 / v - 1 / 5

Please help...

Answer 1

Your questions are very hard to read.  For instance, I presume your first one is 7/(3y + 5).  In other words, I presume the "+ 5" is also in the denominator.  Most of your other questions have the same ambiguity.  You might want to use parentheses to make sure we know what's where.

For your first (assuming I'm right):  you're concerned about the denominator becoming 0, because one cannot divide by 0.  So, find out where that happens:

3y + 5 = 0

3y = -5

y = -5/3

So, the rational expression is undefined where y = -5/3

For the second: First off, the thing you're dividing by cannot be 0.  That means t cannot be 0.  Also, from the thing you're dividing by, t cannot be -2 because that would make the denominator 0.  For the other fraction, you'll need to factor it.  Technically, you only need to factor the denominator:

t^2 + 3t - 10 = (t + 5)(t - 2)

t = 2 and t = -5 will make the denominator 0.  Now:  Some of these factors will cancel out when you carry out the division.  This is irrelevant.  If any denominator ever goes to 0, the whole thing is undefined.  So, the correct answer is t cannot be -5, -2, 0 or 2.  If you carry out the division, though, you get (t + 2)/(t - 2), as you indicated.  For this specific rational function, the only restriction is that t cannot be 2.  Take the answer you think most likely.

One cannot simplify by removing factors of 1.  You've made a mistake somewhere.  However, your simplification is correct.

For the last one - well, here's a place where your not using parentheses makes it hard to know where to begin.  Is the 1/5 a separate fraction?  Or is it in the denominator of the first one, as (v - 1/5)?  Or is the fraction 9/(v - 1)/5?  That's three different problems.  I'm going to assume it's:

1/v = (9/v) - (1/5)

The quickest way to do this is to carry out the subtraction.  You'll need a common denominator.  Fortunately, that's easy.  The common denominator is just 5v.  So it becomes:

1/v = (45/5v) - (v/5v) = (45 - v)/5v

Multiply through by 5v:

5 = 45 - v

Rearrange:

v = 40

and you're done.  Obviously, if I've misread your problem, then that's the wrong answer.