Divide the expression
$(a x + b y + b x + a z + a y + b z) by (a + b) .$

(x + y + z)

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(x + y + b)

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(x + y + a)

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(x + y)

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Solution

The correct option is A $(x + y + z)$
Given: $\frac{a x + b y + b x + a z + a y + b z}{(a + b)}$
Consider the numerator,
$a x + b y + b x + a z + a y + b z = (a x + a y + a z) + (b x + b y + b z)$
Taking 'a' common from the first group and 'b' common from the second group, we get
$= a (x + y + z) + b (x + y + z)$
$= (x + y + z) (a + b)$
Therefore,
$\frac{a x + b y + b x + a z + a y + b z}{(a + b)} = \frac{(x + y + z) (a + b)}{(a + b)} = (x + y + z)$

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