solve and check the equation for x. I just can not figure this out.
5/x+6 + 2/x^2+7x+6 = 3/x+1
Thanks!
Use parentheses to tell us whether you mean
2/(x^2 + 7x + 6) or 2/x^2 +7x +6
and also whether you mean
(3/x) + 1 or 3/(x+1)
and also
(5/x)+6 or 5/(x+6)
also go to myalgebra com and solve it for free on that calculator since I also can not clarify your intended question.
To solve the equation 5/x + 6 + 2/(x^2 + 7x + 6) = 3/(x+1), we first need to simplify it. Let's start by finding a common denominator for the fractions.
The common denominator for the terms 5/x, 6, and 2/(x^2 + 7x + 6) is x(x^2 + 7x + 6) since it contains both x and x^2 + 7x + 6.
Now, let's rewrite the equation with the common denominator:
[(5)(x^2 + 7x + 6)]/[(x)(x^2 + 7x + 6)] + [(6)(x)(x^2 + 7x + 6)]/[(x)(x^2 + 7x + 6)] + [(2)(x)]/[(x)(x^2 + 7x + 6)] = [(3)(x)]/[(x+1)]
Simplifying further:
(5x^2 + 35x + 30 + 6x(x^2 + 7x + 6) + 2x)/(x(x^2 + 7x + 6)) = (3x)/(x+1)
Expanding the expression:
(5x^2 + 35x + 30 + 6x^3 + 42x^2 + 36x + 2x)/(x(x^2 + 7x + 6)) = (3x)/(x+1)
Combining like terms:
(6x^3 + 47x^2 + 73x + 30)/(x(x^2 + 7x + 6)) = (3x)/(x+1)
Now, we need to solve for x. Let's start by multiplying both sides of the equation by x(x^2 + 7x + 6) to get rid of the denominators:
[(6x^3 + 47x^2 + 73x + 30)/(x+1)]*x(x^2 + 7x + 6) = 3x(x^2 + 7x + 6)
Simplifying:
(6x^3 + 47x^2 + 73x + 30)*[(x)(x^2 + 7x + 6)] = 3x(x^2 + 7x + 6)
Expanding and simplifying further:
[6x^4 + 47x^3 + 73x^2 + 30x + 42x^3 + 329x^2 + 510x + 180]/(x+1) = 3x^3 + 21x^2 + 18x
Combining like terms and simplifying:
6x^4 + 89x^3 + 402x^2 + 660x + 180 = 3x^3 + 21x^2 + 18x(x + 1)
Rearranging the equation and setting it equal to zero:
6x^4 + 89x^3 + 402x^2 + 660x + 180 - 3x^3 - 21x^2 - 18x - 18x^2 - 18x = 0
Combining like terms:
6x^4 + 66x^3 + 363x^2 + 624x + 180 = 0
At this point, the equation is a quartic equation and solving it directly can be complex. It's best to use a graphing calculator or an algebraic software to find the approximate solutions or roots. You can try using the provided link to myalgebra.com to help you solve the equation or consult any other appropriate mathematical software or calculator.