Question

f(x)=√x-6 - 4/√5-x
f(x)=√x+1 - 7x+8/x²+4x
срочно надо пожалуйста
20балов даю
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Answer 1

To simplify these expressions, let's go step by step:

1) Simplifying f(x) = √x - 6 - 4/√(5-x):

To simplify this expression, we need to have a common denominator for the fraction. The common denominator is √(5-x), so we can rewrite the expression as:

f(x) = (√x * √(5-x) - 6√(5-x))/√(5-x) - 4/√(5-x)

Now, let's simplify the numerator of the fraction:

f(x) = (√x * √(5-x) - 6√(5-x))/√(5-x) - 4/√(5-x)
f(x) = (√(x*(5-x)) - 6√(5-x))/√(5-x) - 4/√(5-x)
f(x) = (√(5x-x^2) - 6√(5-x))/√(5-x) - 4/√(5-x)

Now, we can combine the terms:

f(x) = (√(5x-x^2) - 6√(5-x) - 4)/√(5-x)

So, the simplified expression is f(x) = (√(5x-x^2) - 6√(5-x) - 4)/√(5-x).

2) Simplifying f(x) = √x+1 - (7x+8)/(x^2+4x):

To simplify this expression, we first need to find a common denominator for the fraction.

f(x) = √x+1 - (7x+8)/(x^2+4x)
f(x) = √x+1 - (7x+8)/(x(x+4))

Now, let's simplify the numerator of the fraction:

f(x) = √x+1 - (7x+8)/(x(x+4))
f(x) = √x+1 - (7x+8)/x(x+4)
f(x) = √x+1 - (7x+8)/(x^2+4x)

Now, we can combine the terms:

f(x) = (√x+1*(x^2+4x) - (7x+8))/x(x+4)
f(x) = (√(x+1)*(x^2+4x) - (7x+8))/x(x+4)

So, the simplified expression is f(x) = (√(x+1)*(x^2+4x) - (7x+8))/x(x+4).