How to simplify expressions?

How would you simplify these rational expressions?

• I have to simplify and find the excluded value of rational expressions but I didn't understand it when the teacher explained it to me. Here are a few of the questions... . 44 'x' to the third (cubed) over 24 'x' (44 x^3/24 x) .3 'y' + 6 over 'y' + 2 (3y+6/y+2) .3 'a' - 15 over 4 'a' - 20 (3a-15/4a-20) .2 'b' - 8 over 4 - 'b' (2b-8/4-b) .'r' squared - 2 'r' - 15 over 'r' squared + 'r' -6 (r^2-2r-15/r^2+r-6) .'s' + 3 over 2 's' squared + 3 's' - 4 (s+3/2s^2+3s-4) .2 'm' squared + 8 'm' - 24 over 3 'm' cubed + 24 'm' squared + 36 (2m^2+8m-24/3m^3+24m^2+36) .6 'n' cubed - 18 'n' squared over 3 'n' cubed - 27 'n' (6n^3-18n^2/3n^3-27^n) I'm really having a hard time with this. If you could solve at least one and explain how that would be great.

• Answer:

  For 3 'a' - 15 over 4 'a' - 20 (3a-15/4a-20), make it so that it is 3(a-5)/4(a-5). So now it would be 3/4. You put it into distributive property and cancel out the ones that match. .'r' squared - 2 'r' - 15 over 'r' squared + 'r' -6 (r^2-2r-15/r^2+r-6). For the numerator you have to factor. Last year, (I'm in geometry this year) my teacher taught me the X Method. In this method you make so that the r^2 is on the left side of the X, so it would be 'r' on the top left and 'r' on the bottom left. Next you want to put the number without a variable on the right side of the X, BUT it has to multiply into each other, like 3 and 4 would make 12. So now you'd put -5 on the top right and 3 on the bottom right. Then multiply the ones that connect (bottom left with top right, bottom right with top left) The add them together and you'd get number in the middle. The put the variable next to each other (top with top and bottom with bottom) in parentheses. Now do that with bottom and cancel the ones that match. ____r___ -5 ____\__/ _____\ / _____/\_____________________-5r+3r=-2r ____/__\ ___/____\__________________What you should get __/______\_________________(r-5)(r+3) r_________3 Sorry if it looks bad doesn't work with spaces well.