The given expression is-
[tex]\frac{6c^2d^5}{2c}-\frac{2c^{10}}{d^{-2}}[/tex]
We can solve this using the cross method to subtract the fractions. The following property shows this method.
[tex]\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{c\cdot d}[/tex]
Using this property, we have
[tex]\frac{6c^2d^5d^{-2}-2c^{10}2c}{2c\cdot d^{-2}}[/tex]
Now, we solve the products.
[tex]\frac{6c^2d^3-4c^{11}}{2cd^{-2}}[/tex]
We simplify the terms since all of them can be divide by 2c
[tex]\frac{3cd^3-2c^{10}}{d^{-2}}[/tex]
At last, we use the negative exponent property. This property allows us to change the position of the power with negative exponent.
[tex]d^2\cdot(3cd^3-2c^{10})[/tex]
At last, we solve this product using the distributive property.
Therefore, the equivalent expression is
[tex]3cd^5-2cd^2[/tex]
