Home > Algebra > Addition and Subtraction of Rational Expressions

How do you combine #2/(4z^2-12z+9)-(z+1)/(2z^2-3z)#?

Answer 1

Isaiah Anthony

#(-2z^2+3z+3)/(z(2z-3)(2z-3))#

In a question involving algebraic fractions, no matter what the operation is, factorize first.

#2/(4z^2-12z+9)-(z+1)/(2z^2-3z)#

#2/((2z-3)(2z-3)) - (z+1)/(z(2z-3))" "larr #find the LCD

=#(2z -(z+1)(2z-3))/(z(2z-3)(2z-3)) " "larr# make equivalent fractions

#(2z -(2z^2-3z+2z-3))/(z(2z-3)(2z-3))" "larr# simplify the numerator

#(2z -2z^2+3z-2z+3)/(z(2z-3)(2z-3))#

#(-2z^2+3z+3)/(z(2z-3)(2z-3))#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Nathan Axel

To combine the given expressions, we need to find a common denominator. The common denominator for the two expressions is (4z^2-12z+9)(2z^2-3z).

Next, we multiply the first fraction by (2z^2-3z)/(2z^2-3z) and the second fraction by (4z^2-12z+9)/(4z^2-12z+9).

After multiplying and simplifying, we can combine the numerators over the common denominator.

The resulting expression is (2(2z^2-3z)-(z+1)(4z^2-12z+9))/(4z^2-12z+9)(2z^2-3z).

Further simplification may be possible depending on the specific values of z.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.