Factor the denominators and multiply both sides of the equation by the least common denominator.
x=2 and x=-1
Practice makes perfect
We want to solve the given rational equation.
1/x+x/2=x+4/2x
Let's begin by highlighting the all of the different factors in the denominators. This will help us find the least common denominator (LCD).
1/x+x/2=x+4/2x
⇕
1/x+x/2=x+4/2 xWe will solve the equation by multiplying each side by the LCD of the denominators.
Note that we have a quadratic equation now. Let's identify the values of a, b, and c.
x^2-x-2=0 ⇔ 1x^2 +( -1)x+(-2)=0
We have that a= 1, b= -1, and c=-2. Let's substitute these values into the Quadratic Formula and solve for x.
Let's calculate both solutions by using the positive and negative signs.
x=1 ± 3/2
x=1+ 3/2
x=1- 3/2
x=4/2
x=- 2/2
x=2
x=-1
Finally, we will check if either x=2 or x=-1 is an extraneous solution. To do this, we need to substitute 2 and -1 for x in the original equation. Let's start with x=2.
