Simplify (x² + 5x -14) / (x - 2)?

Question

Simplify (x² + 5x -14) / (x - 2)


Simplify c^3 - c
---------
4c + 4

Simplify 7a 64b
------ * -------
(4b)^3 21a^4


I am having problem simplying. Please teach me the process so I could understand it better.

Answer 1

(x+7)(x-2)/(x-2) the (x-2) reduce to 1 so simplified (x+7)
but remember x cannot =2

factor out the c and get c(c^2-1)
that factors to c(c-1)(c+1) since c^2-1 is the difference of two squares

4c+4 =4(c+1)

7a 64b....typo not sure what is being asked

for that or the next

Answer 2

Simplify (x² + 5x -14) / (x - 2)
= [(x+7)(x-2)]/(x-2) = x+7


(c^3 - c)/4c+4
= [c(c-1)(c+1)]/4(c+1) = c(c-1)/4

(7a 64b)/[(4b)^3 * 21a^4]
= 7*a*64b/64b^3*21*a^4
= 1/3b^2a^3

Answer 3

You need to factor the numerators and denominators first before simplifying.

First One: numerator is a simple trinomial (look for numbers that add to 5 and multiply to -14)

[(x - 2)(x + 7)]/(x - 2) now divide out common factor
= x + 7

Second one: numerator is common factoring followed by diff of squares factoring and the denominator is common factoring:

[c(c^2 - 1)]/[4(c + 1)]
=[c(c+1)(c - 1)]/{4(c+1)}
= [c(c-1)]/4

The third one is hard to follow but I think it is multiplying. Multiply numerators and denominators together after simplifying.

7a/ 64b^3 times 64b/21a^4

the 64s divide out as does the 7 with the 21 which becomes a 3

(ab)/(3a^4b^3) <--- now you can divide out common ab
= 1/(3a^3b^2)

Answer 4

A. (x+7)
B . [c(c+1)] / 4
C. 1/(3a^3 b^2)