MAJOR MATH HELP! Dividing rational expressions and Solving rational equations?

Question

Dividing Rational Expressions
__1__ + __1__
(c-d) (d-c)



__6__ + ___8__
(5y²-45) ( 3-y)


__10__ - ___6b___
(a-b) ( a ² - b ²)

Solving Rational Equations

_3_ - __4r__ = -4
(4r) (r -3)

_3__ ∕ _4x_ = 4
(4x) (x-3)

_u__ - _2u___ = _u²___
(u+2) (2-u) (u²-4)



Thank you so much! I put the denominators in brackets because they bunch up for some reason.

Answer 1

1/(c-d) + 1/(d-c) = 1/(c-d) - 1/(c-d) = 0

6/(5y^2-45) + 8/(3-y) = 6/(5(y^2-9)) + 8/(3-y) =
6/(5(y-3)(y+3)) - 8/(y-3) =
(6/5)/(y-3)(y+3)) - 8(y+3)/((y-3)(y+3) =
( (6/5) - 8(y+3) ) / ( (y-3)(y+3) ) =
( (6/5) - 8y -24 ) / ( (y-3)(y+3) ) =

Answer 2

the basic technique is the same as adding fractions of integers: get a least common denominator.

1/(c-d) + 1/(d-c) = 1/(c-d) + -1/(c-d) = (1-1)/(c-d) = 0

6/(5y^2-45) + 8/(3-y) = 6/(5y^2-45) + 8(-5)(y+3)/(5y^2-45)
=(6 -40y -120)/(5y^2-45) = (-40y-114)/(5y^2-45)

10/(a-b) - 6b/(a^2-b^2) = 10(a+b)/(a^2-b^2)- 6b/(a^2-b^2)
= (10a +10b - 6b)/(a^2-b^2) = (10a + 4b)/(a^2-b^2)

3/4r -4r/(r-3) = -4 multiply by LCD 4r(r-3)
3(r-3) -4r(4r) = -4(4r(r-3))
3r-9-16r^2 = -16r^2+48
3r=57
r=19

now do the rest yourself.

Answer 3

1/(c-d) + 1/(d-c) =
1/(c-d) -1/(c-d) = 0

6/(5y²-45) + 8/( 3-y) =
6/5(y+3)(y-3) - 8/(y-3) =
6/5(y+3)(y-3) - 8*5(y+3)/5(y+3)(y-3) =
(6 + 40y + 120) / 5(y+3)(y-3) =
(40y + 126) / 5(y+3)(y-3)

10/(a-b) - 6b/ ( a ² - b ²) =
10(a+b) / ( a ² - b ²) - 6b/ ( a ² - b ²) =
(10a + 4b) / ( a ² - b ²)

and so forth