How do you find the excluded value and simplify # (3x^2-5x-28)/(x^2+3x-28)#?

Question

Hazel Anglin · Accepted Answer

#(3x+7)/(x+7)# #(3x^2-5x-28)/(x^2+3x-28)# =#(3x^2-12x+7x-28)/(x^2+7x-4x-28)# =#[3x*(x-4)+7*(x-4)]/[x*(x+7)-4*(x+7)]# =#[(3x+7)(x-4)]/[(x-4)(x+7)]# =#(3x+7)/(x+7)#

Isaiah Anthony · Answer

#=(3x+7)/(x+7) = 1 + (2x)/(x+7)# #Nr = 3x^2-5x-28= 3x^2-12x+7x-28# #=3x(x-4)+7(x-4) = (x-4)(3x+7)# #Dr = x^2+3x-28=x^2+7x-4x-28# #=x(x+7)-4(x+7)=(x-4)(x+7)# #Nr/Dr = (cancel(x-4)(x+7)) /(cancel(x-4)(4x+7)# #=(3x+7)/(x+7) = 1 + (2x)/(x+7)#

Avery Alexander · Answer

undefined To find the excluded value, we need to determine the values of x that would make the denominator equal to zero. In this case, the denominator is (x^2+3x-28). To find the excluded value, we set the denominator equal to zero and solve for x.

(x^2+3x-28) = 0

Factoring the quadratic equation, we have:

(x+7)(x-4) = 0

Setting each factor equal to zero, we get:

x+7 = 0   or   x-4 = 0

Solving for x, we find:

x = -7   or   x = 4

Therefore, the excluded values are x = -7 and x = 4.

To simplify the expression (3x^2-5x-28)/(x^2+3x-28), we can divide both the numerator and denominator by the greatest common factor (GCF) of the terms. In this case, the GCF is 1.

Simplifying the expression, we get:

(3x^2-5x-28)/(x^2+3x-28) = (3x^2-5x-28)/(x+7)(x-4)

Avery Alexander · Answer

undefined To find the excluded value for the expression (3x^2 - 5x - 28) / (x^2 + 3x - 28), we need to determine the values of x that would make the denominator zero, as division by zero is undefined. To find these values, we set the denominator equal to zero and solve for x.

The denominator is x^2 + 3x - 28. Setting this expression equal to zero, we get:

x^2 + 3x - 28 = 0

Now, we can factor the quadratic equation or use the quadratic formula to solve for x.

Factoring:
(x + 7)(x - 4) = 0

Setting each factor equal to zero:
x + 7 = 0  -->  x = -7
x - 4 = 0  -->  x = 4

So, the excluded values for this expression are x = -7 and x = 4.

To simplify the expression, we can factor both the numerator and the denominator, then cancel out common factors if they exist. After that, we rewrite the expression in its simplest form.