Question

X/(x+5) +(x+5)/(x-5) = 50/(x^2 -25)​

Answer 1

Ответ:  х=2.5

Объяснение:

х\х+5 + х+5\х-5=50\х^2-25       х не равно -5, х не равно 5

х\х+5 + х+5\х-5 - 50\х^2-25=0

х\х+5 + х+5\х-5 - 50\(х-5)(х+5)=0

х(х-5)+(х+5)^2-50\ (х-5)(х+5)=0

х^2+5х-10х+(х+5)^2-50\ (х-5)(х+5)=0

х(х+5)-10(х+5)+(х+5)^2\(х-5)(х+5)=0

(х+5(х-10+х+5)\(х-5)(х+5)=0

2х-5\х-5=0

2х-5=0

х=5\2

х=2,5

Answer 2

To solve the given equation:

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x/(x+5) + (x+5)/(x-5) = 50/(x^2 - 25)

Let's start by finding a common denominator for all the fractions on the left-hand side:

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Common denominator = (x+5)(x-5)

Now, we'll rewrite the fractions with the common denominator:

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x(x-5)/[(x+5)(x-5)] + (x+5)^2/[(x+5)(x-5)] = 50/[(x+5)(x-5)]

Simplify the fractions:

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x(x-5) + (x+5)^2 = 50

Expand and simplify:

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x^2 - 5x + x^2 + 10x + 25 = 50

Combine like terms:

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2x^2 + 5x + 25 = 50

Subtract 50 from both sides:

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2x^2 + 5x - 25 = 0

Now, we have a quadratic equation. We can solve it using the quadratic formula:

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x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 2, b = 5, and c = -25. Plugging in these values:

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x = (-5 ± √(5^2 - 4 * 2 * -25)) / (2 * 2)
x = (-5 ± √(25 + 200)) / 4
x = (-5 ± √225) / 4
x = (-5 ± 15) / 4

This gives us two possible solutions:

1. x = (10) / 4 = 2.5
2. x = (-20) / 4 = -5

So, the solutions to the equation are x = 2.5 and x = -5.