SOLUTION: Could you please help me solve this equation?
2x^2-x-9/(x+1)(x^2+5)=A/x+1+Bx+C/x^2+5
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Question 151164: Could you please help me solve this equation?
2x^2-x-9/(x+1)(x^2+5)=A/x+1+Bx+C/x^2+5
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.
Multiply every term by the LCD . This will cancel out the denominators.
Multiply and simplify.
FOIL
Distribute
Take note that the terms on the right side are and . So this means that and . So the first equation is
Also, notice how the terms on the right side are and . So this means that and . So the second equation is
Finally, notice how the constant terms on the right side are and . So this means that . So the third equation is
Start with the first equation.
Subtract B from both sides.
Move onto the third equation
Plug in
Distribute
Subtract 10 from both sides.
So we now have the system of equations
Use any method to solve the system, to get the solutions:
and
Start with the given equation.
Plug in
Subtract
-----------------------------------------
Answer:
So the answers are
, , and
Which means that
Note: to check your answer, graph the left side and the right side. The two functions should be the same graph.
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