# rational expressions

• Dec 20th 2006, 01:19 PM
mathnoobie25
rational expressions
if someone could help me with these seven HW problems. i had do do 75 of them, i just cant figure out these 7! help is much needed..thanks you so much!

Simplify
#1. 6t^2-7t-5 all over 2t+1

#2 q^2-11q+30 Divided by q^2-2q-24
------------- -----------
2q^2-7q-15 q^2-q-20

#3 4x+12 over 3-x minus 3x+15 over 3-x

#4 x+3 over x^2-3x-10 minus 2 over x-5

#5 x^-2-y^-2 over y^-1-x^-1

Solve the Equation

#6 3x over x^2-9 Plus 1 over x-3 = 3 over x+3

Word Problem

#7 Following a severe snowstorm, Ken and Bettina must clear their driveway and sidewalk. Ken can clear the snow by himself in 4 hours, and bettina can clear the snow be herself in 6 hours. After bettina has been working for 3 hours, ken is able to join her. how much longer will it take them working together to remove the rest of the snow.

Any help would be much appreciated. Thank You!
• Dec 20th 2006, 01:27 PM
earboth
Quote:

Originally Posted by mathnoobie25
...

Simplify
#1. 6t^2-7t-5 all over 2t+1

...

Hello,

$\frac{6t^2-7t-5}{2t+1}=\frac{(2t+1)(3t-5)}{2t+1}=3t-5\ , \ t \neq -\frac{1}{2}$

EB
• Dec 20th 2006, 01:35 PM
earboth
Quote:

Originally Posted by mathnoobie25
...
Simplify

#2 q^2-11q+30 Divided by q^2-2q-24
------------- -----------
2q^2-7q-15 q^2-q-20

...

Hello,

$\frac{q^2-11q+30}{2q^2-7q-15} \div \frac{q^2-2q-24}{q^2-q-20}=$

$\frac{(q-6)(q-5)}{(q-5)(2q+3)} \div \frac{(q-6)(q+4)}{(q-5)(q+4)}=$. Now transform into a product:

$\frac{(q-6)(q-5)}{(q-5)(2q+3)} \cdot\frac{(q-5)(q+4)}{(q-6)(q+4)}= \frac{q-5}{2q+3}$

EB
• Dec 20th 2006, 01:38 PM
earboth
Quote:

Originally Posted by mathnoobie25
...
Simplify

#3 4x+12 over 3-x minus 3x+15 over 3-x

...

Hello,

$\frac{4x+12}{3-x} - \frac{3x+15}{3-x}=\frac{x-3}{3-x}=-1$

EB
• Dec 20th 2006, 01:43 PM
earboth
Quote:

Originally Posted by mathnoobie25
...

Simplify

#4 x+3 over x^2-3x-10 minus 2 over x-5
...

Hello,

$\frac{x+3}{x^2-3x-10} - \frac{2}{x-5}=\frac{x+3}{(x-5)(x+2)} - \frac{2}{x-5}=$ $\frac{x+3}{(x-5)(x+2)} - \frac{2(x+2)}{(x-5)(x+2)}$

$=\frac{-x-1}{(x-5)(x+2)}$

EB
• Dec 20th 2006, 01:49 PM
earboth
Quote:

Originally Posted by mathnoobie25
...
Simplify

#5 x^-2-y^-2 over y^-1-x^-1

...

Hello,

$\frac{x^{-2} - y^{-2}}{y^{-1} - x^{-1}}=\frac{(x^{-1}-y^{-1})(x^{-1}+y^{-1})}{y^{-1} - x^{-1}}=$ $=-(x^{-1}+y^{-1})$

EB
• Dec 20th 2006, 01:56 PM
earboth
Quote:

Originally Posted by mathnoobie25
...

Solve the Equation

#6 3x over x^2-9 Plus 1 over x-3 = 3 over x+3

...

Hello,

I assume that you know: $x^2-9=(x+3)(x-3)$

$\frac{3x}{x^2-9}+\frac{1}{x-3}=\frac{3}{x+3}$. Multiply by (x^2-9) (it's the common denominator) and cancel the equal factors out(?):

$3x+x+3=3(x-3)$. Solve for x. I've got x = -12.

EB

PS: to #7. It's raining here, no snow in sight - and by the way it is very late and I'm afraid that I'll make some silly mistakes. So I leave #7 for someone else.
• Dec 21st 2006, 12:15 AM
earboth
Quote:

Originally Posted by mathnoobie25
...
Word Problem

#7 Following a severe snowstorm, Ken and Bettina must clear their driveway and sidewalk. Ken can clear the snow by himself in 4 hours, and bettina can clear the snow be herself in 6 hours. After bettina has been working for 3 hours, ken is able to join her. how much longer will it take them working together to remove the rest of the snow. ...

Hello and good morning,

let S be the total amount of snow which has to be removed

then
Ken removes $\frac{S}{4}$ in 1 hour
Bettina removes $\frac{S}{6}$ in 1 hour

The complete work could be described by:

$\underbrace{\frac{S}{6} \cdot 3}_{\text{ Bettina working alone}} + \underbrace{\left(\frac{S}{4}+\frac{S}{6} \right) \cdot x}_{\text{B.+K. working together}} =S$. Divide by S:

$\frac{1}{2}+\frac{5}{12}x=1$. Solve for x. I've got x = 1.2 hours = 1 hour 12 minutes.

EB