Question

HELP FOR A MEDAL AND FAN. :)

Answer 1

Show all steps to simplify and solve each of the following rational expressions:

Answer 2

HI :D

Answer 3

1. (2x+6)/(3x-1)+(x-5)/(3x-1)

Factor out the GCF of 2 from each term in the polynomial.
(2(x)+2(3))/(3x-1)+(x-5)/(3x-1)

Factor out the GCF of 2 from 2x+6.
(2(x+3))/(3x-1)+(x-5)/(3x-1)

The numerators of expressions that have equal denominators can be combined. In this case, (2(x+3))/((3x-1)) and ((x-5))/((3x-1)) have the same denominator of (3x-1), so the numerators can be combined.
(2(x+3)+(x-5))/(3x-1)

Simplify the numerator of the expression.
(2x+6+x-5)/(3x-1)

Combine all similar terms in the polynomial 2x+6+x-5.
(3x+1)/(3x-1)

Answer 4

2. (3)/(y+4)-(2)/(y)

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of y(y+4). The (3)/((y+4)) expression needs to be multiplied by ((y))/((y)) to make the denominator y(y+4). The -(2)/(y) expression needs to be multiplied by ((y+4))/((y+4)) to make the denominator y(y+4).
(3)/(y+4)*(y)/(y)-(2)/(y)*(y+4)/(y+4)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of y(y+4).
(3(y))/(y(y+4))-(2)/(y)*(y+4)/(y+4)

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of y(y+4).
(3(y))/(y(y+4))-(2(y+4))/(y(y+4))

The numerators of expressions that have equal denominators can be combined. In this case, (3(y))/(y(y+4)) and -((2(y+4)))/(y(y+4)) have the same denominator of y(y+4), so the numerators can be combined.
(3(y)-(2(y+4)))/(y(y+4))

Simplify the numerator of the expression.
(3y-2y-8)/(y(y+4))

Since 3y and -2y are like terms, add -2y to 3y to get y.
(y-8)/(y(y+4))

Answer 5

3. (z^(2))/(z+4)-(16)/(z+4)

Combine all similar expressions in the polynomial.
(z^(2)-16)/(z+4)

The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).
((z-4)(z+4))/(z+4)

Reduce the expression by canceling out the common factor of (z+4) from the numerator and denominator.
((z-4)<X>(z+4)<x>)/(<X>(z+4)<x>)

Reduce the expression by canceling out the common factor of (z+4) from the numerator and denominator.
(z-4)

Remove the parentheses around the expression z-4.
z-4

Answer 6

do you understand it?

Answer 7

Yes! thank you so much. c: i get it now!