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Объяснение:

1.

42m⁴/n⁵ :(6mn)=42m⁴/n⁵ • 1/6mn=

=7m³/n⁶

1 — Б

2.

(2аb-b²)/9 • 3a/b=(b(2a-b))/9 • 3a/b=

=(a(2a-b)/3=(2a²-ab)/3

2 — A

3.

(3a-1)/(4-b) + (2a+3)/(b-4)=

=(3a-1)/(4-b) + (2a+3)/(-(4-b))=

=(3a-1)/(4-b) - (2a+3)/(4-b)=

=(3a-1-2a-3)/(4-b)=(a-4)/(4-b)

3 — A

4.

1/a - 6/(a²+6a)=1/a - 6/(a(a+6))=

=(a+6-6)/(a(a+6))=a/(a(a+6))=1/(a+6)

4 — Б

1.

а)

(а²-b)/(a²-9b²) + (9b²-3b)/(9b²-a²)=

=(a²-b)/(a²-9b²) + (9b²-3b)/(-(a²-9b²))=

=(a²-b)/(a²-9b²) - (9b²-3b)/(a²-9b²)=

=(a²-b-9b²+3b)/(a²-9b²)=

=(a²+2b-9b²)/(a²-9b²)

б)

(4а²-bc)/(4a²-b²) + (2ac-b²)/(b²-4a²)=

=(4a²-bc)/(4a²-b²) + (2ac-b²)/(-(4a²-b²))=

=(4a²-bc)/(4a²-b²) - (2ac-b²)/(4a²-b²)=

=(4a²-bc-2ac+b²)/(4a²-b²)

2.

a)

1/(a+2) - 2/3a=(3a-2(a+2))/(3a(a+2))=

=(3a-2a-4)/(3a²+6a)=(a-4)/(3a²+6a)

б)

(15а-13b)/(3a+b) - (10a-b)/(2a)=

=((15a-13b)•2a-(10a-b)(3a+b))/(2a(3a+b))=

=(30a²-26ab-(30a²+10ab-3ab-b²))/(6a²+2ab)=

=(30a²-26ab-30a²-10ab+3ab+b²)/(6a²+2ab)=

= (-33ab+b²)/(6a²+2ab)

в) на листочке