Just the work for 4 algebra questions?

Question

i've already found the answers i just need the work written out, please help this is the only thing i have trouble with

show factoring

1. 10x^2 - 30x + 20 / x^2 - 1 = 10 (x-2) / x+1

2. b / b-1 + 2b / b^2 - 1 = b (b+3) / (b+1)(b-1)

3. x^3 + 2x^2 + x - 6 / x - 1 = x^2 + 3n + 9

4. n^3 - 27 / n - 3 = n^2 + 3n + 9

Answer 1

First one: Numerator becomes 10(x^2 + 3x + 2) after you factor out a 10.

Now, the trinomial x^2 +3x +2 can factor into (x+1)(x+2)

So the numerator becomes 10(x+1)(x+2)

The denominator is a difference of perfect squares, and so quickly factors to:

(x+1)(x-1)

Leaving the fraction:

10(x+1)(x+2)

-------------------

(x+1)(x-1)

The (x+1)s cancel, and you're home free.

If you don't know how to factor trinomials, this is gonna be a big pain for you.

Anyway.

b / (b-1) + 2b/(b^2-1)

You're adding fractions. You need to find a common denominator.

Since b^2-1 = (b+1)(b-1) [that difference of squares again...] and the denominator of the OTHER fraction is (b-1) all we need to do to get a common denominator is multiply the first fraction by (b+1)/(b+1) (which is equal to one, and won't change the value of the fraction, just its appearance).

b(b+1) over (b+1)(b-1)  plus 2b over (b+1)(b-1)

We have:

b^2 + b + 2b

-------------------

(b+1)(b-1)

And the top is just:

b(b+1+2) or b(b+3)

As for #3 I think you put part of number 4 on the right hand side.

4:

n^3 -27 is a difference of cubes, and factors to (n-3)(n^2+3n+9)

If we're dividing that by (n-3) we're just left with n^2+3n + 9

It really helps to have these special things (like difference of squares, difference of cubes) memorized at least until you're done with calculus.