SOLUTION: Please help me solve this equation:
\frac{6x^2 + 6x + 42}{(x+5)(x + 2)(x - 4)} - \frac{6}{x+5}
Answer should be written as:
\frac{a}{x^2+bx+c}
Here a,b and c are ordina
Algebra.Com
Question 88539: Please help me solve this equation:
\frac{6x^2 + 6x + 42}{(x+5)(x + 2)(x - 4)} - \frac{6}{x+5}
Answer should be written as:
\frac{a}{x^2+bx+c}
Here a,b and c are ordinary numbers.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
(x+2)(x-4)} - \frac{6}{x + 5})
(x+2)(x-4)} - \left(\frac{(x+2)(x-4)}{(x+2)(x-4)}\right)\left(\frac{6}{x + 5}\right))
Multiply the second fraction by (x-4)}{(x+2)(x-4)})
(x+2)(x-4)} - \left(\frac{6(x+2)(x-4)}{(x+5)(x+2)(x-4)}\right))
(x+2)(x-4)} - \left(\frac{6(x^2-2x-8)}{(x+5)(x+2)(x-4)}\right))
Foil
(x+2)(x-4)} - \left(\frac{6x^2-12x-48}{(x+5)(x+2)(x-4)}\right))
Distribute
-(6x^2-12x-48)}{(x+5)(x+2)(x-4)})
Combine the fractions
(x+2)(x-4)})
Distribute the negative
(x+2)(x-4)})
Combine like terms
}{(x+5)(x+2)(x-4)})
Factor out an 18
(x-4)})
Reduce
Foil the denominator
So
simplifies to
As always, you can verify by graphing the original and the simplified expressions to compare them
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