Home > Precalculus > Partial Fraction Decomposition (Linear Denominators)

How do you solve #\frac { w } { w - 3} - \frac { 5w } { 5w - 2} = \frac { w - 2} { 5w ^ { 2} - 17w + 6}#?

Answer 1

Chloe Alexander

#w=-1/6#

The fractions on the left should first be combined:

#w/(w-3)-(5w)/(5w-2)=(w-2)/(5w^2-17w+6)#

#(w(5w-2))/((5w-2)(w-3))-((5w)(w-3))/((5w-2)(w-3))=(w-2)/(5w^2-17w+6)#

#((5w^2-2w))/((5w-2)(w-3))-((5w^2-15w))/((5w-2)(w-3))=(w-2)/(5w^2-17w+6)#

#(13w)/(5w^2-17w+6)=(w-2)/(5w^2-17w+6)#

Assuming equal denominators, we can state:

#13w=w-2#

#12w=-2=>w=-1/6#

Now let's make sure that value isn't disallowed by the denominator. Remember that we had #w# terms in the denominator, so any value of #w# that results in a denominator of 0 can't be allowed.

#w!=3, 2/5#

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

Answer 2

Chloe Alexander

To solve the equation (\frac{w}{w - 3} - \frac{5w}{5w - 2} = \frac{w - 2}{5w^2 - 17w + 6}), follow these steps:

Find a common denominator for all fractions.
Multiply both sides of the equation by this common denominator to clear the fractions.
Simplify the resulting equation.
Solve for (w).
Check for any extraneous solutions.

The solution to the equation is (w = 1) or (w = \frac{3}{5}).

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.