Posted by Jetta on .
Multiplying and Dividing Rational Expressions:
2) x^28x+7/x^2+6x7 = (x7)/(x+7)
3) x^25x+6/x+4 times 3x+12/x2 =3(x3)
4)2x3/5x+1 divided by 6x^213x+6/15x^27x2=1
5) x^39x/x^2+11x+24 times x^2+7x8/x^24x+3= x(x3)(x1)/(x+3)(x+8)
6) 4x8/x^2x6 divided by x^3 +x^26x/x^29=(x3)/x(x2)
7) x^216/x3 divided x+4/x^29=(x1)/(x+1)

math 
Jetta,
are they correct?

math 
Henry,
4. (2X3)/(4X1) Div by (6X^213X+6)/
(15X^27X2).
Factor trinomial in numerator using A*C Method:
A*C = 6*6 = 36 = 4*9,
6X^2 4X9X +6
Group the 4 terms in pairs and factor each pair:
2X(3X2) 3(3X2). Factor out (3x2):
(3X2) (2X3).
Factor the trinomial in denominator
using A*C Method:
A*C = 15*2 =30 = 3*10.
15X^2 +3X10X 2.
Group the 4 terms in pairs and factor each pair:
3x(SX+1) 3(5X+1), Factor out (5x+1):
(5X+1) (3X2).
Write original expression in factored form:
(2X3)/(5X+1) Div by (3X2)(2X3)/
(5X+1)(3X2).
Cancel the (3X2) factors:
(2X3)/5X+1) Div by (2X3)/(5X+1).
Invert divisor and multiply:
(2X3)/(5X+1) * (5X+1)/(2X3).
Cancel the (5X+1) factors:
(2X3)/(2X3) = 1. 
math 
Henry,
5. (X^39)/(X^2+11X+24) * (X^2+7X8_/
(X^24X+3) =
Factor both numerators & denominators:
X(X^29)/(X+3)(X+8) * (X1)(X+8)/
(X1)(X3) =
Cancel factors (X+8), and (X1).
X(X^29)/(X+3) * 1/(X3)
Factor (X^29):
X(X+3)(X3)/(X+3) * 1/(X3).
Cancel factors (x+3) & (X3):
= X. 
math 
Henry,
6.(4X 8)/(X^2 X 6) Div (X^3+X^26X)/
(X^29)
Factor completely:
4(X2)/(X3)(X+2) Div X(X^2+X6)/(X+3)
(X3).
4(X2)/(X3)(X+2) Div X(X+3)(X2)/(X+3)(X3).
Cancel factor (X+3) and invert divisor
4(X2)/(X3)(X+2) * (X3)/X(X2).
Cancel factors (X2), (Z3)
4/X(X+2).