2-(a-1)/(a+2)=(a^a-1)/(a+2)Can you help me solve this problem step by step please?
are you certain it is copied correctly?
I think you meant:
2-(a-1)/(a+2)=(a^2-1)/(a+2)
multiply each term by a+2
2a + 4 - a+1 = a^2-1
a^2 - a -6 = 0
(a-3)(a+2) = 0
a = 3 or a = -2
Sure! Let's solve the given equation step by step.
Step 1: Distribute the denominator on the left side of the equation.
2 - (a - 1)/(a + 2) = (a^(a - 1))/(a + 2)
Step 2: Simplify the expression on the left side.
2 - (a - 1)/(a + 2) = (a^(a - 1))/(a + 2)
To simplify further, we can find a common denominator of (a + 2) for the terms on the left side:
2 * (a + 2)/(a + 2) - (a - 1)/(a + 2) = (a^(a - 1))/(a + 2)
Simplifying the numerator on the left side:
(2a + 4 - a + 1)/(a + 2) = (a^(a - 1))/(a + 2)
(2a - a + 4 + 1)/(a + 2) = (a^(a - 1))/(a + 2)
(a + 5)/(a + 2) = (a^(a - 1))/(a + 2)
Step 3: Cancel out the common denominator (a + 2) on both sides of the equation.
(a + 5) = a^(a - 1)
Step 4: Expand the exponent on the right side.
(a + 5) = a * a^(1 - 1)
(a + 5) = a
Step 5: Simplify the equation.
a + 5 = a
Subtracting 'a' from both sides:
5 = 0
Step 6: Conclusion.
From step 5, we see that the equation is not true for any value of 'a'. Hence, there is no solution to the given equation: 2 - (a - 1)/(a + 2) = (a^(a - 1))/(a + 2)