Question

1) (a^2+ax+x^2/ax+ay)/(a^3-x^3/bx+2by) 2) (4m^2-25n^2/m^3+8)/(2m+5n/m^2-2m+4)

Answer 1

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Answer 2

Let's simplify the given expressions step by step:

1. Simplifying (a^2 + ax + x^2) / (ax + ay):

We can factor out (ax) from the numerator: (a^2 + ax + x^2) = ax(a + 1) + x^2

Now, we can rewrite the expression as: (ax(a + 1) + x^2) / (ax + ay)

Factoring out 'x' from the denominator: (ax(a + 1) + x^2) / x(ax + ay)

Canceling out 'x' from the numerator and the denominator: (a(a + 1) + x) / (a + ay)

The simplified expression is: (a^2 + a + x) / (a + ay)

2. Simplifying (4m^2 - 25n^2) / (m^3 + 8):

The numerator is a difference of squares, so we can factor it using the identity (a^2 - b^2) = (a + b)(a - b): 4m^2 - 25n^2 = (2m + 5n)(2m - 5n)

The denominator is a sum of cubes, so we can factor it using the identity (a^3 + b^3) = (a + b)(a^2 - ab + b^2): m^3 + 8 = (m + 2)(m^2 - 2m + 4)

Now, we can rewrite the expression as: (2m + 5n)(2m - 5n) / (m + 2)(m^2 - 2m + 4)

No further simplification is possible for this expression.