Simplify -(3)/(4r) + 3 - (5)/(6r)-6

Answer 1

To simplify this expression, we can combine like terms.

Starting with the rational terms:

-(3)/(4r) - (5)/(6r)

To combine these, we need to find a common denominator. The common denominator here would be 4r * 6r = 24r^2.

Converting each term to have this common denominator:

-(3 * 6)/(4r * 6) - (5 * 4)/(6r * 4)

Simplifying the numerators:

-(18)/(24r^2) - (20)/(24r^2)

Now, we can combine these terms:

-(18 - 20)/(24r^2)

Simplifying the numerator:

-(-2)/(24r^2) -> (2)/(24r^2) -> (1)/(12r^2)

Now, let's combine this with the rest of the expression:

(1)/(12r^2) + 3 - 6

To combine the rational and integer terms, we need to convert 3 and 6 into fractions with the common denominator of 12r^2:

(1)/(12r^2) + (3 * 12r^2)/(12r^2) - (6 * 12r^2)/(12r^2)

Simplifying the numerators:

(1)/(12r^2) + (36r^2)/(12r^2) - (72r^2)/(12r^2)

Combining the terms:

(1 + 36r^2 - 72r^2)/(12r^2)

Simplifying the numerator:

(-35r^2 + 1)/(12r^2)

Thus, the simplified expression is -(35r^2 - 1)/(12r^2).