Question

1-10/(x-5)=11/(25+x^2-10x)

Answer 1

1-10/(х-5)=11/(х-5)²
(х-5)²-10(х-5)-11=0
х-5=11; х-5=-1
х=16; х=4

ответ: {4;16}

Answer 2

To solve the equation 1 - 10/(x - 5) = 11/(25 + x^2 - 10x), we'll start by simplifying the expression.

1 - 10/(x - 5) = 11/(25 + x^2 - 10x)

First, let's simplify the right side by factoring the denominator:

1 - 10/(x - 5) = 11/[(x - 5)(x - 5)]

Now, let's simplify the left side:

To simplify 10/(x - 5), we can multiply the numerator and denominator by -1 to get -10/-(x - 5), which simplifies to 10/(5 - x) due to the negative sign.

1 - 10/(x - 5) = 1 - 10/(5 - x) = (5 - x)/(5 - x) - 10/(5 - x) = (5 - x - 10)/(5 - x) = (-x - 5)/(5 - x)

Substituting the simplified expressions back into the equation, we have:

(-x - 5)/(5 - x) = 11/[(x - 5)(x - 5)]

Now, we can simplify further by cross-multiplying:

(-x - 5) * [(x - 5)(x - 5)] = 11 * (5 - x)

Expanding both sides:

(-x - 5)(x^2 - 10x + 25) = 55 - 11x

Multiplying out the left side:

-x(x^2 - 10x + 25) - 5(x^2 - 10x + 25) = 55 - 11x

Simplifying:

-x^3 + 10x^2 - 25x + 5x^2 - 50x + 125 = 55 - 11x

Combining like terms:

-x^3 + 15x^2 - 75x + 125 = 55 - 11x

Rearranging terms:

-x^3 + 15x^2 - 75x + 11x + 125 - 55 = 0

Simplifying:

-x^3 + 15x^2 - 64x + 70 = 0

Unfortunately, this equation cannot be solved algebraically using simple methods. To find the solutions, you would need to use numerical methods or graphing techniques.