Home > Algebra > Clearing Denominators in Rational Equations

How do you solve #10/x - 12/(x-3) + 4 = 0#?

Answer 1

Savannah Anderson

You must put on a common denominator.

The LCD (Least Common Denominator) is #x(x - 3)#

#(10(x - 3))/(x(x - 3)) - (12(x))/(x(x - 3)) + (4(x^2 - 3x))/(x xx x - 3) = 0#

Now that the denominators are gone, we can:

#10x - 30 - 12x + 4x^2 - 12x = 0#

#4x^2 - 14x - 30 = 0#

Solve by factoring. Two numbers that multiply to #(-30 xx 4) = -120# and that add to -14 are -20 and 6.

#4x^2 - 20x + 6x - 30 = 0#

#4x(x - 5) + 6(x - 5) = 0#

#(4x + 6)(x - 5) = 0#

# x = -6/4 and 5#

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

Answer 2

Savannah Anderson

To solve the equation 10/x - 12/(x-3) + 4 = 0, you can follow these steps:

Find a common denominator for the fractions. In this case, the common denominator is x(x-3).
Multiply each term by the common denominator to eliminate the fractions.
Simplify the equation by distributing and combining like terms.
Rearrange the equation to isolate the variable on one side.
Solve for x by factoring or using the quadratic formula if necessary.

The final solution will depend on the specific values of x that satisfy the equation.

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.