问题 解答题
下列等式的右边是怎样从左边得到的?
(1)
1
a+b
=
a+b
a2+2ab+b2

(2)
2x(x-y)7
4y(y-x)6
=
x(x-y)
2y

(3)
(a+b)2
a2-b2
=
a+b
a-b

(4)
3
a+b
=
9a(a+b)
3a(a+b)2
答案

(1)分子,分母都乘以(a+b),

1
a+b
=
a+b
a2+2ab+b2
=
1•(a+b)
(a+b)(a+b)
=
a+b
a2+2ab+b2

(2)分子、分母都除以2(x-y)6

2x(x-y)7
4y(y-x)6
=
2x(x-y)7÷2(x-y)6
4y(y-x)6÷2(x-y)6
=
x(x-y)
2y

(3)分子,分母都除以(a+b);

(a+b)2
a2-b2
=
(a+b)2÷(a+b)
(a+b)(a-b)÷(a+b)
=
a+b
a-b

(4)分子,分母都乘以3a(a+b),

3
a+b
=
3×3a(a+b)
(a+b)×3a(a+b)
=
9a(a+b)
3a(a+b)2

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