4x/x+5-x/x-1=3 / дробь

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вопрос

4x/(x+5) - x/(x-1) = 3

To find a common denominator for the fractions, we need to multiply the second term by (x+5) / (x+5) and the first term by (x-1) / (x-1):

[(4x(x-1) - x(x+5)) / ((x+5)(x-1))] = 3

Simplify the numerator:

[(4x^2 - 4x - x^2 - 5x) / ((x+5)(x-1))] = 3

Combine like terms in the numerator:

[(3x^2 - 9x) / ((x+5)(x-1))] = 3

Now, cross-multiply to get rid of the denominator:

3(x+5)(x-1) = 3(3x^2 - 9x)

3(x^2 + 4x - 5) = 9x^2 - 27x

Expand and simplify both sides:

3x^2 + 12x - 15 = 9x^2 - 27x

Rearrange terms:

6x^2 - 39x + 15 = 0

Now, solve this quadratic equation for x using factoring or the quadratic formula.