8. Rational Equations
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Multiply the numerator on the left-hand side by the denominator on the right-hand side, and the denominator on the left-hand side by the numerator on the right-hand side.
x=-2
We will solve the given equation and then check the solutions.
We will solve the rational equation by cross multiplying. If a numerator or denominator contains addition or subtraction, be sure to treat each one as a parenthetical factor in the cross multiplication process.
Cross multiply
Distribute 4
LHS-4x=RHS-4x
Subtract term
.LHS /-2.=.RHS /-2.
We found that x=-2 is a possible solution. Now we have to check it!
We will now check our solution to see whether it is extraneous. To do so, we will substitute x=-2 into the given equation.
x= -2
Add terms
Put minus sign in front of fraction
a/1=a
Calculate quotient
Since we obtained a true statement, x=-2 is a solution of the equation.