Answer:
[tex]\bold{\frac{5d^5-4c^3d^{14}+6c}{c^2d^{10}}}[/tex]
Step-by-step explanation:
[tex]\bold{\frac{75c^2d^{-2}-60c^5d^7+90c^3d^{-7}}{15c^4d^3}}[/tex]
[tex]\bold{75c^2d^{-2}=\frac{75c^2}{d^2}}[/tex]
[tex]\bold{90c^3d^{-7}=\frac{90c^3}{d^7}}[/tex]
[tex]\bold{=\frac{\frac{75c^2}{d^2}-60c^5d^7+\frac{90c^3}{d^7}}{15c^4d^3}}[/tex]
Join[tex]\bold{\:\frac{75c^2}{d^2}-60c^5d^7+\frac{90c^3}{d^7}:\quad \frac{75c^2d^5-60c^5d^{14}+90c^3}{d^7}}[/tex]
[tex]\bold{=\frac{\frac{75c^2}{d^2}-60c^5d^7+\frac{90c^3}{d^7}}{15c^4d^3}}[/tex]
Apply Fraction Rule: [tex]\bold{\frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}}[/tex]
[tex]\bold{=\frac{75c^2d^5-60c^5d^{14}+90c^3}{d^7\cdot \:15c^4d^3}}[/tex]
Factor [tex]\bold{75c^2d^5-60c^5d^{14}+90c^3:\quad 15c^2\left(5d^5-4c^3d^{14}+6c\right)}[/tex]
[tex]\bold{=\frac{15c^2\left(5d^5-4c^3d^{14}+6c\right)}{d^7\cdot \:15c^4d^3}}[/tex]
Cancel [tex]\bold{\frac{15c^2\left(5d^5-4c^3d^{14}+6c\right)}{d^7\cdot \:15c^4d^3}:\quad \frac{5d^5-4c^3d^{14}+6c}{c^2d^7d^3}}[/tex]
[tex]\bold{=\frac{5d^5-4c^3d^{14}+6c}{c^2d^7d^3}}[/tex]
[tex]\bold{c^2d^7d^3=c^2d^{10}}[/tex]
= [tex]\bold{\frac{5d^5-4c^3d^{14}+6c}{c^2d^{10}}}[/tex]
