Simplifying Complex Fractions
[(x+3)/12] / [(4x-5)/15]
[(x+3)/12] x [15/(4x-5)]
(x+3)5/4(3x-5)
(5x+15/12x-20)<-- final answer
Did I do this right. If not could you please explain how to do it correctly
*** final answer
3+5/4(3x-5)
3+5/12x-20
There are typos which make your answer wrong. Starting at
(x+3)5/4(3x-5)
you should have had
(x+3)5 / 4(4x-5)
(5x+15)/(16x-20)
To simplify complex fractions like the one you provided:
1. Start by multiplying the numerator of the complex fraction by the reciprocal of the denominator. In this case, multiply [(x+3)/12] by [15/(4x-5)].
(x+3)/12 * 15/(4x-5)
(x+3)*(15)/(12*(4x-5))
2. Simplify the numerator and denominator separately.
Numerator: (x+3)*(15) = 15x + 45
Denominator: 12*(4x-5) = 48x - 60
3. Rewrite the complex fraction with the simplified numerator and denominator.
(15x + 45)/(48x - 60)
4. If possible, factor out any common factors from the numerator and denominator. In this case, we can divide both the numerator and denominator by 15.
(15/15)x + 45/15) / (48x - 60)/15)
x + 3 / (48x - 60)/15)
x + 3 / (48x - 60)/3)
x + 3 / (16x - 20)
5. Simplify further if necessary. The final answer is:
(x + 3) / (16x - 20)
So, your final answer should be (x + 3) / (16x - 20).