S.Hobden said:
Perform the indicated operations and express answers in simplest terms.
a) (24ab - 8a^2b/ a^2 - 9)=
b)(4x^2 - 10/ x + 3y)*(18y^2 - 2x^2/ 6x^2 - 15)=
c)(-7k / k^2 + k)= (-7k/k^3)?
preform the indicated operation?
i can never remember what to do with each question.
Remove common factors.
24ab - 8a^2b = 8*(3ab - (a^2)b) = 8*a*(3b-ab) = 8*a*b*(3-a)
4x^2 - 10 = 2*(2x^2 - 5)
18y^2 - 2x^2 = 2*(9y^2 - x^2)
6x^2 - 15= 3*(2x^2 - 5)
k^2 + k = k*(k + 1)
Combine LIKE terms.
k^2 + k ≠ k^3 -- k and k^2 are NOT "like terms".
Memorize the "Difference of Squares" factoring.
a^2 - 9 = (a-3)(a+3)
(9y^2 - x^2) = (3y-x)(3y+x)
2x^2 - 5 = \(\displaystyle (\sqrt{2}x-\sqrt{5})(\sqrt{2}x+\sqrt{5})\)
Reduce Fractions
-7k/[k*(k+1)] = (-7/(k+1))*(k/k) = (-7/(k+1))*(1) = -7/(k+1)
When in doubt, add more parentheses to clarify meaning. Some things do not mean what you want.
24ab - 8a^2b/ a^2 - 9 MEANS \(\displaystyle \L\,24ab - \frac{8a^{2}b}{a^{2}} - 9\).
I suspect that is not what you had in mind.
With parentheses, (24ab - 8a^2b)/(a^2 - 9), it means \(\displaystyle \L\,\frac{24ab - 8a^2b}{a^2 - 9}\).
