What is the quotient in simplified form x^2-16/x^2+5x+6

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 344 People

What is the quotient in simplified form? State any restrictions on the variable? \frac{x^2-16}{x^2+5x+6} /\frac{x^2+5x+4}{x^2-2x-8}

Answered by maham237 @ 26/12/2020

$\frac{x^2-16}{x^2+5x+6} / \frac{x^2+5x+4}{x^2-2x-8}$

We can begin by rearranging this into multiplication:

$\frac{x^2-16}{x^2+5x+6} * \frac{x^2-2x-8}{x^2+5x+4}$

Now we can factor the numerators and denominators:

$\frac{(x+4)(x-4)}{(x+3)(x+2)} * \frac{(x-4)(x+2)}{(x+4)(x+1)}$

The factors (x+4) and (x+2) cancel out, leaving us with:

$\frac{(x-4)}{(x+3)} * \frac{(x-4)}{(x+1)}$

Our answer comes out to be:

$\frac{(x-4)^{2} }{(x+3)(x+1)}$ or $\frac{ x^{2} -8x+16}{ x^{2}+4x+3 }$

Based on the numerator of the second fraction (since we used its inverse), the denominators of both, and the factors we canceled out earlier, the restrictions are x ≠ -4, -3, -2, -1, 4

What is the quotient in simplified form x^2-16/x^2+5x+6

Similar Questions

Simplify (6x^-2)^2(0.5x)^4

What is the expression in factored form 4x^2+11x+6

The equation (x+6)^2y+4)^2=36

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.

The graph of f(x) = x2 is translated to form g(x) = (x – 2)2 – 3.

Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?

Simplify the expression –3(x + 3)2 – 3 + 3x. what is the simplified expression in standard form?

Y 1 4 3 x 1 2 in standard form

The quotient of 10 plus x and y minus 3

The quotient of (x4 – 3x2 + 4x – 3) and a polynomial is (x2 + x – 3). what is the polynomial?

The equation of x axis is of the form

Simplify 8y x 3x

2x x 5 in expanded form

Find the simplified form of the difference quotient

What is the simplified form of ? assume x ≠ 0.

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220