Question

(m-2/m+2- m+2/m-2) : 8m/m^2-4

Answer 1

m^2-2m-2m+4-m^2-2m-2m-4=-8m/m^2-4

-8m/m^2-4*m^2-4/8m=-1

Answer 2

To simplify the given expression, let's start by simplifying each fraction separately:

First fraction: (m - 2)/(m + 2) - (m + 2)/(m - 2)

To subtract these fractions, we need a common denominator. In this case, the common denominator is (m + 2)(m - 2).

Applying the common denominator, we have:

[(m - 2)(m - 2) - (m + 2)(m + 2)] / [(m + 2)(m - 2)]

Expanding the numerator:

[m^2 - 4m + 4 - (m^2 + 4m + 4)] / [(m + 2)(m - 2)]

Simplifying the numerator:

[m^2 - 4m + 4 - m^2 - 4m - 4] / [(m + 2)(m - 2)]

Combining like terms:

[-8m] / [(m + 2)(m - 2)]

Simplifying the second fraction: 8m/(m^2 - 4)

Now, let's divide the first fraction by the second fraction:

[-8m / ((m + 2)(m - 2))] / [8m / (m^2 - 4)]

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

[-8m / ((m + 2)(m - 2))] * [(m^2 - 4) / 8m]

Simplifying the expression:

-8m(m^2 - 4) / (8m(m + 2)(m - 2))

Canceling out common factors:

-(m^2 - 4) / (m + 2)(m - 2)

Finally, simplifying the numerator:

-[(m - 2)(m + 2)] / (m + 2)(m - 2)

The (m - 2) and (m + 2) terms cancel out:

-1

Therefore, the simplified expression is -1.