Question

Perform each indicated operation. Then if possible simplify

(x^2-16)÷4x+16/3x^2

Answer 1

(3/4)x^2·(x -4)

Explanation:

What you have written is ...

`(x^2-16)/(4)x+(16)/(3)x^2 = (3x^3+64x^2-48x)/(12)`

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Comment on the given expression

The symbols ÷ and / mean the same thing, unless you specifically say otherwise. Without grouping symbols (parentheses or typeset symbols that show grouping), the order of operations requires that division and exponentiation symbols only apply to the first immediately following operand. That is, 16/3x^2 means (16/3)x^2. If you want 16/(3x^2), you have to write it that way.

Likewise, numerators that consist of summed terms need to be in parentheses.

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We suppose you intend ...

`\displaystyle(x^2-16)/(\left((4x+16)/(3x^2)\right))=(x-4)(x+4)(3x^2)/(4(x+4))\\\\=(3)/(4)x^2(x-4)`