Question

Reduce the following algebraic fractions to the lowest terms.
plz answer
​

Answer 1

Answer:

f. (x^2+10x+21)/(x^2-49)

=(x^2+7x+3x+21)/(x^2-7^2)

=x(x+7)+3(x+7)/(x+7)(x-7)

=(x+7)(x+3)/(x+7)(x-7)

=(x+3)/(x-7)

g. (z^2-2z-8)/(z^2-9z+20)

=(z^2-4z+2z-8)/(z^2-5z-4z+20)

=z(z-4)+2(z-4)/z(z-5)-4(z-5)

=(z-4)(z+2)/(z-5)(z-4)

=(z+2)/(z-5)

h. (x^2-7x-8)/(x^2+3x+2)

=(x^2-8x+x-8)/(x^2+2x+x+2)

=x(x-8)+1(x-8)/x(x+2)+1(x+2)

=(x-8)(x+1)/(x+2)(x+1)

=(x-8)/(x+2)

Answer 2

Anwer:

f.

$\frac{x + 3}{x - 7}$

g.

$\frac{z + 2}{z - 5}$

h.

$\frac{x - 8}{x + 2}$

Step-by-step explanation:

f. x²+10+21

x² - 49

= (x+7) (x+3)

( x+7) (x -7)

= x+3

x - 7

g. z²- 2z -8

z²-9z+20

= (z+2) (z-4)

(z- 5) ( z -4)

= z + 2

z - 5

h