Simplify complex fraction
w+3/4w/w-3 2w
Without providing parentheses and ^ signs for exponents, there are many ways to interpret what you have written. Each gives a different answer.
Do you mean to write
[w + (3/4)w]/(w-3) * 2w ?
Yes, it seems like you want to simplify the complex fraction [w + (3/4)w]/(w-3) * 2w. Let's break it down step by step to simplify it.
Step 1: Simplify the numerator [w + (3/4)w].
To simplify the numerator, we need to find a common denominator for w and (3/4)w. The common denominator is 4, so we can rewrite the numerator as:
[(4w + 3w)/4]
Step 2: Simplify the numerator further.
Combine the terms in the numerator: (4w + 3w) = 7w. Therefore, the numerator simplifies to:
7w/4
Step 3: Combine the numerator and denominator of the complex fraction.
Now, we have:
(7w/4) / (w - 3) * 2w
Step 4: Simplify the complex fraction.
To simplify a complex fraction, we can multiply the numerator and denominator by the reciprocal of the denominator. In this case, the reciprocal of (w - 3) is 1/(w - 3). Therefore, we can rewrite our expression as:
(7w/4) * (1/(w - 3)) * 2w
Step 5: Simplify further.
Multiply the numerators and denominators together:
(7w * 1 * 2w) / (4 * (w - 3))
Simplifying the expression in the numerator gives us:
(14w^2) / (4 * (w - 3))
Step 6: Simplify the expression.
Divide the coefficient and the variable in the numerator and the constant in the denominator by their greatest common factor, which is 2:
7w^2 / (2 * (w - 3))
Therefore, the simplified form of the complex fraction [w + (3/4)w]/(w-3) * 2w is 7w^2 / (2 * (w - 3)).