Simplify these problems:?

Question

1. c² + d / d³ + c² / c^4 + d^4

2. ( mˉ ² + n ˉ ²) / ( mn + mˉ ² n ˉ ²)

3. ( aˉ ² b² / ac ) / ( ab / bˉ ² c³ )

Answer 1

(1)

c² + d / d³ + c² / c^4 + d^4

= c² + 1/d² + 1/c² + d^4

(2)

( mˉ ² + n ˉ ²) / ( mn + mˉ ² n ˉ ²)
=(1/m² + 1/n² ) / (mn + 1/m²n² )

= ((n² +m²) / m²n²) / ( (mn.m²n² + m²n²)/m²n²)
= (n² +m²) / (mn.m²n² + m²n²)
= (n² +m²) / (mn + 1).m²n²

(3)

( aˉ ² b² / ac ) / ( ab / bˉ ² c³ )

= ( aˉ ² b² / ac ) . (bˉ ² c³ / ab)

= (aˉ ².b².bˉ ².c³) / (a² bc)

= (aˉ ².c³) / (a² bc)

= c² / (a².b.a²)

= c² / (a^4.b)

Answer 2

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