Answer:
[tex]\large\boxed{\dfrac{x+4}{4}=\dfrac{y+5}{5}}[/tex]
[tex]\large\boxed{\dfrac{b}{c}=\dfrac{6}{2}}[/tex]
Step-by-step explanation:
[tex]If\ \dfrac{x}{4}=\dfrac{y}{5},\ then\ \dfrac{x+4}{4}=\dfrac{?}{5}\\\\\dfrac{x+4}{4}=\dfrac{x}{4}+\dfrac{4}{4}=\dfrac{x}{4}+1\\\\\text{therefore}\\\\\dfrac{x}{4}=\dfrac{y}{5}\qquad\text{add 1 to both sides}\\\\\dfrac{x}{4}+1=\dfrac{y}{5}+1\\\\\dfrac{x}{4}+\dfrac{4}{4}=\dfrac{y}{5}+\dfrac{5}{5}\\\\\dfrac{x+4}{4}=\dfrac{y+5}{5}[/tex]
[tex]If\ \dfrac{b}{6}=\dfrac{c}{2},\ then\ \dfrac{b}{c}=\dfrac{?}{?}\\\\\dfrac{b}{6}=\dfrac{c}{2}\qquad\text{cross multiply}\\\\2b=6c\qquad\text{divide both sides by 2}\\\\b=3c\qquad\text{divide both sides by }\ c\neq0\\\\\dfrac{b}{c}=3\to\dfrac{b}{c}=\dfrac{6}{2}[/tex]
