[multiplying rational
expressions][section 53]
(1.) 3x - 48y2 3x + 6y
___________ * ____________ here is the problem
2x2 - 8y2 3x + 12y
= 3(x - 16y2) 3(x + 2y)
_________________ *
_______________ factor
2(x2 - 4y2) 3(x + 4y)
= 3(x - 16y2) 3(x + 2y)
______________________ *
_______________
2(x - 2y)(x + 2y) 3(x + 4y) factor
= 3(x - 16y2)
__________________________ cancel and multiply
2(x - 2y)(x + 4y)
(2.) x2 + 8x + 16 x - 3
_____________ * ________ here is the problem
x2 - 9 x + 4
= (x + 4)2 (x - 3) factor
________________ *
____________
(x - 3)(x + 3) (x + 4)
= (x + 4)
___________________ cancel and multiply
(x + 3)
(3.) 9 - x2 x
______ *
_________ here is the problem
x + 3 3 - x
= (3 - x)(3 + x) x
___________________ * _______________
(x + 3) -(x - 3) factor
= -x cancel and multiply
(4.) 24x2 3x - 6
________________ *
_________ here is the
problem
3(x2 - 4x + 4) 2x
= 24x2 3(x - 2)
_______________ * ____________
3(x - 2)2 2x factor
= 12x/(x - 2) cancel and multiply
(5.) 5m + 5n m2 - mn
_________ *
____________ here is the
problem
m2 - n2 (m + n)2
= 5(m + n) m(m - n)
____________________ *
_______________
(m + n)(m - n) (m + n)2 factor
= 5m/(m + n)2 cancel and multiply
(6.) a2 + 6a + 5 5a - 15
_____________ * _______________ here is the problem
a - 3 a2 + 4a - 5
=
(a + 5)(a + 1) 5(a - 3)
__________________ * ________________
(a - 3) (a + 5)(a - 1) factor
= 5(a + 1)/(a - 1) cancel and multiply
(7.) x2 - 3x - 18 3x + 3
________________ * ______________ here is the problem
x2 - x - 2 x2 - 2x - 15
= (x - 6)(x + 3) 3(x + 1)
___________________ *
___________________
(x + 1)(x - 2) (x - 5)(x + 3) factor
= 3(x - 6)
_______________
(x - 2)(x - 5) cancel and multiply
(8.) 4x2 - 9y2 6xy here is the problem
____________________ *
________________
6x2 - 9xy 4xy + 6y2
=
(2x - 3y)(2x + 3y)
6xy
__________________________ *
__________________
3x(2x - 3y) 2y(2x + 3y) factor
= 1 cancel
(9.) a2 + a - 2 a2 - 2a - 8 here is the problem
________________ *
________________
a2 - 3a - 10 a2 - 7a + 12
= (a + 2)(a - 1) (a - 4)(a + 2)
______________________ * _________________
(a - 5)(a + 2) (a - 3)(a - 4) factor
=
(a - 1)(a + 2)
_________________
(a - 5)(a - 3) cancel and multiply
(10.) c2 - 6c c + 3
____________ *
____________ here is the
problem
c - 6 c
= c(c - 6) (c + 3)
____________ * ____________ factor
(c - 6) c
= c + 3 cancel and multiply