Adding fractions and evaluating functions

[Jimmy84]

Homework Statement

1.) (a + 3b) /3ab + (a^2 b - 4ab^2) / 5a^2b^2

2.) n/(m^2) + 3/mn + 2/m


3.) Given F(x) = square root of x + 9 determine F(x+h) - F(x)/h

4.) say whether or not {(x,y) l x= y^2} is a function.

Homework Equations

The Attempt at a Solution

im having problems to find the least common multiple of the algebric expresions in the first two problems.

I think that on problem one the LCM is 15 a^2 b^2

I think that on the second problem the LCM is m^2 (mn) Is this right?


On problem 3 I don't know how to solve (square root of(x+h) +9 - square root of x+9)/ h

How can I solve that? should I use the square root's conjugate? and if so which is it?

Thanks a lot.

 

[w3390]

You're correct about the LCM for problem 1. Recheck what you got for problem 2. You are very close. You have an extra term in it.

 

[Mark44]

Homework Statement

1.) (a + 3b) /3ab + (a^2 b - 4ab^2) / 5a^2b^2

2.) n/(m^2) + 3/mn + 2/m


3.) Given F(x) = square root of x + 9 determine F(x+h) - F(x)/h

4.) say whether or not {(x,y) l x= y^2} is a function.

Homework Equations

The Attempt at a Solution

im having problems to find the least common multiple of the algebric expresions in the first two problems.

I think that on problem one the LCM is 15 a^2 b^2

Right

I think that on the second problem the LCM is m^2 (mn) Is this right?

That's not the least common multiple. The LCM is m²n. Notice that all three denominators divide this evenly.

On problem 3 I don't know how to solve (square root of(x+h) +9 - square root of x+9)/ h

Multiply by 1 in the form of the conjugate over itself. I can't tell you any more because what you wrote is ambiguous. Is it f(x) = sqrt(x + 9) or sqrt(x) + 9?

How can I solve that? should I use the square root's conjugate? and if so which is it?

Thanks a lot.

You didn't ask about 4, but you included it. Graph the relation. If it's a function, no two points will be on the same vertical line.

 

[Jimmy84]

RightThat's not the least common multiple. The LCM is m²n. Notice that all three denominators divide this evenly.
Multiply by 1 in the form of the conjugate over itself. I can't tell you any more because what you wrote is ambiguous. Is it f(x) = sqrt(x + 9) or sqrt(x) + 9?

You didn't ask about 4, but you included it. Graph the relation. If it's a function, no two points will be on the same vertical line.

I ve done the first 2 problems.

On problem 3 I meant sqrt(x + 9) sorry.
Is the conjugate of problem 3 sqrt(x + h + 9) + sqrt(x+9) ?

on problem 4 I considered that x = y^2 could be seen as sqrt x = y which is a function however in the book it said that problem 4 wasent a function. So I am a bit confused about it.

 

[Mark44]

For 3, multiply your expression by 1 in the form of [sqrt(x + h + 9) + sqrt(x+9)] over itself.

For 4, x = y² <==> y = +/-sqrt(x). Now do you understand your book's answer?