Question

Сократите дробь:√x-5/25-x

Answer 1

√x-5/25-x   
√x-5/(5-√x)(5+√x)=-1/(5+√x)

Answer 2

To simplify the given expression, we need to rationalize the denominator. Rationalizing the denominator means eliminating any square roots in the denominator.

The expression is: √x - 5 / (25 - x)

To rationalize the denominator, we'll multiply both the numerator and denominator by the conjugate of the denominator, which is √x + 5. Multiplying by the conjugate will result in the elimination of the square root in the denominator.

√x - 5 / (25 - x) * (√x + 5) / (√x + 5)

Now, apply the distributive property:

(√x - 5)(√x + 5) / ((25 - x)(√x + 5))

Using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), the numerator simplifies:

(√x)^2 - (5)^2 = x - 25

So, the expression becomes:

(x - 25) / ((25 - x)(√x + 5))

Now, we can further simplify it by factoring out -1 from the denominator:

-(x - 25) / ((x - 25)(√x + 5))

Now, the common factor (x - 25) in the numerator and denominator cancels out:

-1 / (√x + 5)

So, the simplified expression is:

-1 / (√x + 5)