# Thread: Need some help simplifying

1. ## Need some help simplifying

Having problems with these 3
1.
x2-x-2 x2-x-20
X
x2+x-6 x2+5x+4 Simplify

2. 1 = 1 6
x-1 2x+3 (2x+3)(x-1) :Solve

3. Brad is (now) 3 years older than janet. Janet's age 2 years from now (future) will be 8/9 of brad's age 2 years from now. How old are they now?

Thanks for any help

2. Originally Posted by ls1ramair19
Having problems with these 3
1.
x2-x-2 x2-x-20
X
x2+x-6 x2+5x+4 Simplify

2. 1 = 1 6
x-1 2x+3 (2x+3)(x-1) :Solve

3. Brad is (now) 3 years older than janet. Janet's age 2 years from now (future) will be 8/9 of brad's age 2 years from now. How old are they now?

Thanks for any help
Can you rewrite problems 1 and 2 please. For x squared write x^2. and for something divided by something write something/something. 'cause the forum right aligns everything, so its distorted and i really dont know what's going on.

For 3. though:

Let x be Brad's age. Then x - 3 is Janet's age. 2 years from now, Janet will be x - 3 + 2 = x - 1 = (8/9)(x + 2) = (8x + 16)/9

So the equation we want to solve is x - 1 = (8x + 16)/9.
=> 9x - 9 = 8x + 16
=> x = 25

So their ages now are, Brad: 25, Janet 22.

3. 1.
x^2-x-2 Times x^2-x-20
x^2+x-6SPACE x^2+5x+4 Simplify

2.
1/x-1= 1/2x+3 + 6/(2x+3)(x-1) solve:

4. Originally Posted by ls1ramair19
1.
x^2-x-2 Times x^2-x-20
x^2+x-6SPACE x^2+5x+4 Simplify

2.
1/x-1= 1/2x+3 + 6/(2x+3)(x-1) solve:

1. (x^2 - x - 2)/(x^2 + x - 6) times (x^2 - x - 20)/(x^2 + 5x + 4)

=> [(x - 2)(x + 1)]/[(x - 2)(x + 3)] times [(x - 5)(x + 4)]/[(x + 1)(x + 4)]

The (x - 2)'s cancel from the first fraction and the (x + 4)'s cancel from the second.

So we have (x + 1)/(x + 3) times (x - 5)/(x + 1)
=> [(x + 1)(x - 5)]/[(x + 1)(x + 3)]

The (x + 1)'s cancel leaving (x - 5)/(x + 3)

2. 1/(x - 1) = 1/(2x + 3) + 6/(2x + 3)(x - 1)
multiplying through by (2x + 3)(x - 1) we obtain:

2x +3 = x - 1 + 6
=>2x + 3- x = -1 + 6
=> x = 2

5. Originally Posted by ls1ramair19
1.
x^2-x-2 Times x^2-x-20
x^2+x-6SPACE x^2+5x+4 Simplify

2.
1/x-1= 1/2x+3 + 6/(2x+3)(x-1) solve:

If you dont see why i multiplied by (2x + 3)(x - 1) in 2. An alternate method may help you see why.

What you could do is bring the 1/(2x +3) over the equal sign to obtain:

1/(x - 1) - 1/(2x +3) = 6/(2x + 3)(x - 1)

we see if we add the left side, we will get a fraction where the lcm is the same as the right, so the denominators of both fractions will be the same, so the numerators can be equated. So we would end up with the line:

2x + 3 - x + 1 = 6
=> x = 2

6. Thank you very much you explained it a lot better than my teacher could

7. Originally Posted by ls1ramair19
Thank you very much you explained it a lot better than my teacher could
I hope so. Don't just read through it though. Try to work through it. Try both methods and see which one you like better. and then if you come up on any problems, just post a reply.