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.
4
Practice makes perfect
We will solve the given equation and then check the solutions.
2x+4/x-3=3x/x-3
Let's do these two things one at a time!
Solving the Equation
We will solve the rational equation by using the Cross Products Property. If a numerator or denominator contains addition or subtraction, be sure to treat each one as a parenthetical factor in the cross multiplication process.
We obtained a quadratic equation. Let's identify the values of a, b, and c.
x^2-7x+12=0 ⇕ 1x^2+( - 7)x+ 12=0
We see that a = 1, b = - 7, and c = 12. Next, we will substitute these values into the Quadratic Formula.
We will find the values for x by using the positive and the negative signs.
x=7± 1/2
x=7+ 1/2
x=7- 1/2
x=8/2
x=6/2
x=4
x=3
We found that x=4 and x=3 are possible solutions. Now we have to check them!
Checking the Solutions
We check our solutions to see whether any of them are extraneous. To do so, we will substitute x=4 and x=3 into the given equation. Let's start with x=4.
