SOLUTION: Please help me solve these rational equation: x^4+2x^2= x/x+2+3/x+3=13/x^2+5x+6

Question 117610: Please help me solve these rational equation:
x^4+2x^2=
x/x+2+3/x+3=13/x^2+5x+6
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

Do you want to factor x^4+2x^2?

Start with the given expression

Factor out the GCF

#2

Start with the given expression

Factor the denominator on the right side

Multiply both sides by the LCD . Notice how every denominator is eliminated

Distribute and multiply

Distribute again

Subtract 13 from both sides

Combine like terms

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our answer is
or

Notice if we graph and we can see that they intersect at and . So this visually verifies our answer. note: Ignore the vertical lines. They are not part of the graph.

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