Question

M^5+m^4+m^3/m^3+m^2 * m^5+m^4/m^4+m^3+m^2

Answer 1

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Answer 2

To simplify the expression, let's first factor out the common terms in each fraction. The expression is:

(M^5 + M^4 + M^3) / (M^3 + M^2) * (M^5 + M^4) / (M^4 + M^3 + M^2)

Now, let's simplify each fraction separately:

1. (M^5 + M^4 + M^3) / (M^3 + M^2): Factor out M^3 from the numerator: M^3 * (M^2 + M + 1) / (M^3 + M^2)

2. (M^5 + M^4) / (M^4 + M^3 + M^2): Factor out M^4 from the numerator: M^4 * (M + 1) / (M^4 + M^3 + M^2)

Now, the simplified expression is:

[M^3 * (M^2 + M + 1) / (M^3 + M^2)] * [M^4 * (M + 1) / (M^4 + M^3 + M^2)]

Next, we can cancel out common factors in the numerator and denominator:

M^3/M^3 = 1, and (M^2 + M + 1)/(M^2) = 1 + M^(-1) + M^(-2)

The expression becomes:

1 * [M^4 * (M + 1) / (M^4 + M^3 + M^2)]

Now, let's factor out common terms again:

M^4 * (M + 1) = M^5 + M^4

So, the final simplified expression is:

(M^5 + M^4) / (M^4 + M^3 + M^2)