Question

(a-c)/(a-√2a)*(a-2)/(√a-√c)*(√2-(√2a)/√a+√2))

Answer 1

(2b-b^2+a-b/2(a+b))*2ab

(2b/a-b^2-1/2)*2ab= (4b-2ab^2-a)/2a*2ab=  (4b-2ab^2-a)*b=4b^2-2ab^3-ab

Answer 2

To simplify the expression, let's take it step by step:

1. First, let's simplify the expression (a - √2a) in the denominator: (a - √2a) = a(1 - √2)

2. Now, let's simplify the expression (√a - √c) in the middle part of the expression: (√a - √c) = √(a) - √(c)

3. Next, let's simplify the expression (√2 - (√2a)/(√a + √2)): √2 - (√2a)/(√a + √2)

To simplify the above expression, let's rationalize the denominator by multiplying both the numerator and the denominator by (√a - √2): √2 - (√2a)/(√a + √2) * (√a - √2)/(√a - √2)

Expanding the numerator: √2 * (√a - √2) - (√2a) * (√a - √2)

Expanding the denominator: (√a + √2) * (√a - √2)

Simplifying the expression further: √2√a - 2 - (√2a√a - √2*√2a) / (√a)^2 - (√2)^2

√2√a - 2 - (√2a√a - 2√a) / a - 2

√2√a - 2 - (√2 * a - 2√a) / a - 2

√2√a - 2 - (√2a - 2√a) / a - 2

√2√a - 2 - (-√2√a) / a - 2

√2√a - 2 + √2√a / a - 2

Now, simplify (√2√a - 2 + √2√a): 2√2√a - 2 / a - 2

Factor out 2 from the numerator: 2(√2√a - 1) / a - 2

4. Now, let's put all the simplified expressions back together:

(a - √2a) / (a - √2a) * (a - 2) / (√a - √c) * (√2 - (√2a) / (√a + √2))

= [a(1 - √2)] / [2(√2√a - 1) / (a - 2)]

Invert the denominator and multiply: = [a(1 - √2)] * [(a - 2) / 2(√2√a - 1)]

Now, you can further simplify or leave the expression in this form, depending on the context or specific requirements of the problem you are working on.