Solve y-4c^-1/(y-2c^-1)(y+2c^-1)

$$\frac { y - 4 c ^ { - 1 } } { ( y - 2 c ^ { - 1 } ) ( y + 2 c ^ { - 1 } ) }$$

Evaluate

$$\frac{c\left(cy-4\right)}{\left(cy\right)^{2}-4}$$

Solution Steps

Consider \left(y-2c^{-1}\right)\left(y+2c^{-1}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{y-4c^{-1}}{y^{2}-\left(2c^{-1}\right)^{2}}$$

Expand \left(2c^{-1}\right)^{2}.

$$\frac{y-4c^{-1}}{y^{2}-2^{2}\left(c^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{y-4c^{-1}}{y^{2}-2^{2}c^{-2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{y-4c^{-1}}{y^{2}-4c^{-2}}$$

Expand

$$\frac{yc^{2}-4c}{\left(cy\right)^{2}-4}$$

Solution Steps

Consider \left(y-2c^{-1}\right)\left(y+2c^{-1}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{y-4c^{-1}}{y^{2}-\left(2c^{-1}\right)^{2}}$$

Expand \left(2c^{-1}\right)^{2}.

$$\frac{y-4c^{-1}}{y^{2}-2^{2}\left(c^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{y-4c^{-1}}{y^{2}-2^{2}c^{-2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{y-4c^{-1}}{y^{2}-4c^{-2}}$$