help with rational algebraic expressions?

Question

simplify:

<1.>
k^2-5k+4
-------------
k^2+2k-3





<2.>
a^2+4a-5
------------
a^3-a






<3.>
t^2-9
--------
t^3-6t^2+9t






<4.>
2x^2+5x-3
--------------
1-4x^2









<5.>
16-9b^2
-------------
3b^2+11b-20









<6.>
c^2-d^2
------------
c^2+2cd+d^2




<7.>
y^4-16
-----------
(y+2)^2(y^2+4)






please help me :)
thank you very much!

Answer 1

You have to factor each part then cancel common factors on top & bottom. Example:

k^2-5k+4
-------------
k^2+2k-3


(k-4)(k-1)
------------
(k+3)(k-1)


(k-4)
------
(k+3)

where k does not equal 1 or -3 (which would give 0 on the bottom of a fraction)

Answer 2

I'll solve the #1-3 & you solve the rest.

1. (k^2 - 5k + 4)/(k^2 + 2k - 3)

First: factor the numerator & denominator.....

[(k - 4)(k - 1)]/[(k + 3)(k - 1)]

Sec: cancel "like" terms....

= (k - 4)/(k + 3)

2. (a^2 + 4a - 5)/(a^3 - a)

First: factor....

[(a+5)(a-1)]/[(a(a^2 - 1)]

Sec: continue to factor ("a^2-1" is the difference of squares)....

[(a + 5)(a - 1)]/[a(a + 1)(a - 1)]

Third: cancel "like" terms....

= (a + 5)/[a(a + 1)]

3. (t^2 - 9)/(t^3 - 6t^2 + 9t)

First: factor....

[(t + 3)(t - 3)]/[(t - 3)(t - 3)]

Sec: cancel "like" terms....

= (t + 3)/(t - 3)

Answer 3

1) (k-4)/(k+3)
2) (a+5)/(a^2+a)
3) (t+3)/[t(t-3)]
4)-(x+3)/(1+2x)
5) -(4+3b)/(x+5)
6) (c-d)/(c+d)
7) (y-2)/(y+2)

Answer 4

ok for starters rational skill that's written as a fragment 4/a million is 4, 4 is rational. As for algebraic expressions that merely skill there's a variable, 'x' and no equivalent sign 4x+a million. Now to multiply those including "(4x+a million)"and (2x+a million), you're able to use certainly one of two procedures (be conscious it extremely is not 8x+a million). the fundamentals are merely multiply '4x' and the '2x+a million' to get '8x(the x squared)+4x' and then upload that to the made of 'a million' (the 2d quantity interior the 1st equation) situations the entire 2d equation to get '2x+a million'. including '8x(squared)+4x+2x+a million' and including it jointly you get 8x(squared)+6x+a million.

Answer 5

1. (k-4)(k-1) ; (k-1)(k+3)
2. (a+5)(a-1) ; (a^2-a)(a+1)
3. (t-3)(t+3) ; (t^2-3t)(t-3)