How do you solve #a/(a-5)+2=(3a)/(a+5)#?
Given:
Check by substituting back in the original equation:
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To solve the equation (a/(a-5)) + 2 = (3a)/(a+5), you can follow these steps:
- Start by multiplying both sides of the equation by (a-5)(a+5) to eliminate the denominators.
- Simplify the equation by distributing and combining like terms.
- Rearrange the equation to isolate the variable, a.
- Solve for a by continuing to simplify and solve the resulting equation.
- Check your solution by substituting the value of a back into the original equation to ensure it satisfies the equation.
The detailed steps are as follows:
-
Multiply both sides of the equation by (a-5)(a+5): (a/(a-5)) * (a-5)(a+5) + 2(a-5)(a+5) = (3a/(a+5)) * (a-5)(a+5)
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Simplify the equation by distributing and combining like terms: a(a+5) + 2(a-5)(a+5) = 3a(a-5)
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Rearrange the equation to isolate the variable, a: a^2 + 5a + 2(a^2 - 25) = 3a^2 - 15a
-
Solve for a by continuing to simplify and solve the resulting equation: a^2 + 5a + 2a^2 - 50 = 3a^2 - 15a 3a^2 - a^2 - 5a + 15a - 2a^2 + 50 = 0 0a^2 + 10a + 50 = 0 10a + 50 = 0 10a = -50 a = -5
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Check your solution by substituting the value of a back into the original equation: (-5/(-5-5)) + 2 = (3(-5)/(-5+5)) (-5/-10) + 2 = (-15/0)
Simplifying further, we get: 1/2 + 2 = undefined
Since the right side is undefined, the equation has no solution.
Therefore, the equation (a/(a-5)) + 2 = (3a)/(a+5) has no solution.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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