x^2+12/((x^2+x)) =8- x

Question

PLease can you help me solve this equation.

Answer 1

Sure--at least I'll get you started.

First, multiply all terms by (x²+x) to CLEAR fractions, giving

x⁴+x³+12 = 8x²-x³+8x-x²

 

Next, collect like terms; you get a 4th degree polynomial = 0, which by inspection has 1 as a root (since sum of all coefficients & the constant) is 0.

 

Synthetic division by 1 gives 0 remainder, of course, and the depressed polynomial is x³+4x²+x-6 = 0 and here again 1 is a root, so 1 should be divided out synthetically again, and you wind up with a depressed polynomial of degree 2 which can be solved.