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How do you simplify #(6w^2+11w-7)/(6w-3)# and what are the restrictions?

Answer 1

Factor #y = 6x^2 + 11x - 7.# Converted #y' = x^2 + 11x - 42#. Factor pairs of -42 ->(-2, 21)(-3, 14) Then, p' = -3, and q' = 14 Then, #p = -3/6 = -1/2#, and #q = 14/6 = 7/3# #y = (x - 1/2)(x + 7/3) = (2x - 1)(3x - 7)#

#f(x) = ((2x - 1)(3x - 7))/(3(2x - 1)) = (3x - 7)/3#

Limitation: (2x -1) cannot equal zero or x cannot equal half.

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Answer 2

Jace Anderson

To simplify the expression (6w^2+11w-7)/(6w-3), you can use polynomial long division or synthetic division. The simplified form is w + 2 with no remainder.

The restrictions for this expression are that w cannot equal 1/2, as it would result in division by zero.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.