Solve the equation. Check the solution.
a over a sqaured minus thirty-six plus two over a minus six equals one over a plus six + start fraction 2 over a minus 6 end fraction = start fraction 1 over a plus 6 end fraction
Unfortunately, the equation provided cannot be solved as it contains multiple equal signs and incomplete expressions. Please provide the complete and correct equation.
learn how to type math and fractions, and we can talk.
If this is what you meant, then use a common denominator of (a+6)(a-6) to get
a/(a^2-36) + 2/(a-6) = 1/(a+6) + 2/(a-6)
a + 2(a-6) = (a-6) + 2(a+6)
3a-12 = 3a+6
no solution
so fix your problem and we can try again.
As an AI language model, I did not provide any problem. However, if you meant fractions or Math equations, you can use symbols and formatting options available on most text editors or word processors. For example, for fractions, you can use the `/` symbol or the fraction option to create a fraction symbol. For Math equations, you can use subscript and superscript options, square root symbols, integrals, summation, and other mathematical operators.
If you provide a specific problem or equation, I can provide a solution or steps to follow.
To solve the given equation, let's simplify both sides of the equation first.
Starting with the left-hand side (LHS):
a/a^2 - 36 + 2/(a - 6)
To add the fractions with different denominators, we need a common denominator. In this case, the common denominator would be (a^2 - 36)(a - 6):
a(a - 6)/(a(a - 6)) - 36(a - 6)/(a(a - 6)) + 2(a^2 - 36)/(a(a - 6))
= (a^2 - 6a - 36a + 216 + 2a^2 - 72)/(a(a - 6))
= (3a^2 - 42a + 144)/(a(a - 6))
Moving on to the right-hand side (RHS):
1/a + 2/(a - 6)
To add the fractions with different denominators, we need a common denominator. In this case, the common denominator would be a(a - 6):
(a - 6)/[a(a - 6)] + 2/a(a - 6)
= (a - 6 + 2a)/(a(a - 6))
= (3a - 6)/(a(a - 6))
Now, we have:
(3a^2 - 42a + 144)/(a(a - 6)) = (3a - 6)/(a(a - 6))
To eliminate the denominators, we can cross-multiply:
(3a^2 - 42a + 144)(a)(a - 6) = (3a - 6)(a)(a - 6)
Expanding both sides further:
(3a^2 - 42a + 144)(a^2 - 6a) = (3a - 6)(a^2 - 6a)
Using the distributive property, we get:
3a^4 - 30a^3 - 42a^3 + 252a^2 + 144a^2 - 864a = 3a^3 - 6a^2 - 18a^2 + 36a
Combining like terms:
3a^4 - 72a^3 + 396a^2 - 900a = 3a^3 - 24a^2 + 36a
Bringing all terms to one side, we have:
3a^4 - 75a^3 + 420a^2 - 936a = 0
At this point, we have transformed the given equation into a quartic equation.
To solve the equation, we can factor out common terms:
3a(a^3 - 25a^2 + 140a - 312) = 0
Now, we have two possibilities:
1. 3a = 0 ---> a = 0
2. (a^3 - 25a^2 + 140a - 312) = 0
To solve the cubic equation (a^3 - 25a^2 + 140a - 312) = 0, we can use numerical methods like Newton's method or synthetic division to find the approximate solutions.
Once we find the solutions for the cubic equation, we can combine them with the solution a = 0, and substitute them into the original equation to check if they satisfy the equation.
Therefore, further calculations are required to find the complete solution of the given equation and to check the solutions.