Question

Which expression is equal to c2−4c+412c3+30c2÷c2−46c4+15c3?

Answer 1

A:
`(c(c-2))/(2(c+2))`

Explanation:

`(c^(2) -4c+4)/(12c^(3) + 30c^(2))` ÷
`(c^(2) -4)/(6c^(4) + 15c^(3))`

expand.

= [c^2 - 2×2×c + 2^2] / [6×(c^2)×(2c + 5)] ÷ [c^2 - 2^2] / [3×(c^3)×(2c +5)]

factorize.

= [(c-2)^2] / [6×(c^2)×(2c + 5)] ÷ [(c-2)(c+2)] / [3×(c^3)×(2c +5)]

multiply by the reciprocal.

= [(c-2)^2] / [6×(c^2)(2c + 5)] × [3(c^3)(2c +5)] / [(c-2)(c+2)]

= [(c-2)×3(c^3)] / [6×(c^2)×(c+2)]

= [c×(c-2)] / [2×(c+2)]

= A:
`(c(c-2))/(2(c+2))`

Answer 2

A: c (c-2)/ 2 (c +2)

Explanation:

Which is equal to c^2-4c+4/ 12c^3+ 30c^2 divided by c^2-4/ 6c^4 +15c^3?

A: c (c-2)/ 2 (c +2)

B: 2 (c-2)/ c(c+2)

C: 2 (c+2)/ c(c-2)

D: c(c+2)/ 2(c-2)

[c^2 - 4c + 4] / [12×(c^3) + 30×(c^2)] ÷ [c^2 - 4] / [6×(c^4) +15×(c^3)]

Expand the expression

= [c^2 - 2×2×c + 2^2] / [6×(c^2)×(2c + 5)] ÷ [c^2 - 2^2] / [3×(c^3)×(2c +5)]

Factorize the expression

= [(c-2)^2] / [6×(c^2)×(2c + 5)] ÷ [(c-2)(c+2)] / [3×(c^3)×(2c +5)]

Multiply by interchanging the numerator and denominator of the divisor

= [(c-2)^2] / [6×(c^2)(2c + 5)] × [3(c^3)(2c +5)] / [(c-2)(c+2)]

= [(c-2)×3(c^3)] / [6×(c^2)×(c+2)]

= [c×(c-2)] / [2×(c+2)]

= c(c - 2) / 2(c + 2)

[c^2 - 4c + 4] / [12×(c^3) + 30×(c^2)] ÷ [c^2 - 4] / [6×(c^4) +15×(c^3)] = c(c - 2) / 2(c + 2)