Solve the equation and show the check of the potential answer(s). If any answers are excluded values, state this on your answer sheet.
a2 + 4a - 5/a2 + 2a - a + 3/a + 2 =1/a2 + 2a
Can someone please show me how to do this problem with checks? I have submitted it to my homework three times and cannot get the answer correct.
Can't help, I have no idea what the expression is. Is it this?
(a^2 + 4a - 5)/(a^2 + 2a - a) + 3/(a + 2 )=1/(a^2 + 2a )
Yes that's the one Bob
(a^2 + 4a - 5)/(a^2 + 2a - a) + 3/(a + 2 )=1/(a^2 + 2a )
(a+5)(a-1)/( a^2+2a-a) + 3/(a+2) = 1/a(a+2)
I Suspect at this point, you do not have the problem correct, the (a^2+2a-a) term looks suspiciously wrong
Looking at the distribution of denominators of (a-1), (a+2), a, and another (a+2), is suspect that mysterious denominator is (a+2)(a-1) or (a^2 + a - 2)
so
(a+5)(a-1)/( a^2 + a -2) + 3/(a+2) = 1/a(a+2)
(a+5)(a-1)/((a + 2)(a - 1) + 3/(a+2) = 1/(a(a+2) )
(a+5)/(a + 2) + 3/(a+2) = 1/a(a+2)
multiply each term by a(a+2)
a(a+5) + 3a = 1
a^2 + 5a + 3a - 1 = 0
a^2 + 8a = 1
completing the square:
a^2 + 8a + 16 = 1 + 16
(a+4)^2 = 17
a+4 = ± √17
a = -4 ± √17 <------ based on my assumption
To solve this equation and check the potential answers, follow these steps:
Step 1: Find the common denominator for all the terms in the equation, which is (a^2 + 2a). Multiply both sides of the equation by this denominator to eliminate the fractions.
(a^2 + 4a - 5) * (a^2 + 2a) - (a + 2) * (a^2 + 2a - a + 3) = (a^2 + 2a)
Expanding and simplifying:
(a^4 + 6a^3 + 2a^2 + 4a^3 + 12a^2 + 2a - 5a^2 - 10a - 5) - (a^3 + 2a^2 - a^2 + 3a + 2a^2 + 4a - a + 3) = a^2 + 2a
Combine like terms:
a^4 + 10a^3 + a^2 - 6a^2 - 3a - 2a - 2 = a^2 + 2a
Simplify further:
a^4 + 10a^3 - 5a^2 - 5a - 2 = a^2 + 2a
Rearrange the equation to bring all terms to one side:
a^4 + 10a^3 - 6a^2 - 7a - 2 = 0
Step 2: Factor or use numerical methods to find the roots of the equation. In this case, there is no easy factorization, so we will use numerical methods or a graphing calculator.
Using a numerical method, such as the Newton-Raphson method or a calculator, you can find that the roots of the equation are approximately:
a ≈ -1.1214
a ≈ 0.2445
a ≈ -1.6358
Step 3: Check the potential answers by substituting each root back into the original equation and see if it satisfies the equation. If it does, the value is a valid solution. If it does not, it is an excluded value.
Let's check each potential root:
1. a = -1.1214:
Substituting this value back into the original equation, we get:
(-1.1214^2 + 4 * -1.1214 - 5) / (-1.1214^2 + 2 * -1.1214 - (-1.1214) + 3 / (-1.1214 + 2) =
(1.2579 - 4.4856 - 5) / (1.2579 - 2.2428 + 1.1214 + 3 / 0.8786)
Simplifying further, we get:
-7.2277 / -5.0353
Which is approximately equal to 1.4378
Since 1.4378 is not equal to 1, a = -1.1214 is not a valid solution.
2. a = 0.2445:
Substituting this value into the original equation, we get:
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