Simplify the following expression:
0.7+0.4
0.7
2
+(0.4+0.2)(0.7)+(0.4×0.2)
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Let a=0.7 and b=0.4.
Notice that the given expression has a form resembling algebraic identities. Let's rewrite the numerator using a=0.7, b=0.4, and let c=0.2.
The numerator is:

a
2
+(b+c)a+bc=a
2
+ab+ac+bc=a(a+b)+c(a+b)=(a+b)(a+c)
Substituting the actual values back:
a=0.7
b=0.4
c=0.2

So, the numerator becomes:

(0.7+0.4)(0.7+0.2)=(1.1)(0.9)
The given expression is:

0.7+0.4
(0.7+0.4)(0.7+0.2)
​

Canceling out the common term (0.7+0.4) from both the numerator and denominator:

=0.7+0.2=0.9