How do you simplify #(x+3) /( x+1) div (x^2+5x+6)#?

Answer 1

Savannah Anderson

In cases like this you try to factorise and cancel

#=cancel(x+3)/(x+1)-:cancel((x+3))(x+2)#

#=1/(x+1)*1/(x+2)#

#=1/((x+1)(x+2))=1/(x^2+3x+2)#

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Answer 2

Jameson Allen

To simplify the expression (x+3) / (x+1) ÷ (x^2+5x+6), we can follow these steps:

Factorize the denominator (x^2+5x+6) into two binomial factors: (x+2)(x+3).
Rewrite the expression as multiplication: (x+3) / (x+1) * 1 / [(x+2)(x+3)].
Simplify the expression by canceling out common factors: 1 / (x+1) * 1 / (x+2).
Combine the fractions by multiplying the numerators and denominators: 1 / [(x+1)(x+2)].

Therefore, the simplified expression is 1 / [(x+1)(x+2)].

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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.