Question

Perform the indicated operations and simplify the expression: (frac5b/4a^2 - 9b^2 + frac4/2a - 3b).

a) (frac4/a + 3b)
b) (frac4/a - 3b)
c) (frac4/2a - 3b)
d) (frac4/4a - 3b)

Answer 1

To simplify the given expression, we combine like terms and rewrite the expression with a common denominator. After simplifying and combining like terms, we get the expression (frac{10ab - 36b^2 + 8a - 12ab^2}{4a^3}).

Step-by-step explanation:

To simplify the expression (frac{5b}{4a^2} - 9b^2 + frac{4}{2a} - 3b), we can combine like terms. The first step is to rewrite the expression with a common denominator. The common denominator is 4a^2, so we multiply each term by the appropriate fraction to get:

(frac{5b}{4a^2})(frac{2a}{2a}) - 9b^2(frac{4}{4a^2}) + frac{4}{2a} - 3b(frac{4a^2}{4a^2})

This simplifies to:

frac{10ab}{4a^3} - frac{36b^2}{4a^2} + frac{4}{2a} - frac{12ab^2}{4a^2}

Next, we combine like terms:

frac{10ab}{4a^3} - frac{36b^2}{4a^2} + frac{4}{2a} - frac{12ab^2}{4a^2} = frac{10ab - 36b^2 + 8a - 12ab^2}{4a^3}

So the simplified expression is (frac{10ab - 36b^2 + 8a - 12ab^2}{4a^3}).