Solve frac{abc^{2}-10abcd}{3b^2c^2-6b^2cd}*12bc^2d/10acd

$$\frac { a b c ^ { 2 } - 10 a b c d } { 3 b ^ { 2 } c ^ { 2 } - 6 b ^ { 2 } c d } \times \frac { 12 b c ^ { 2 } d } { 10 a c d }$$

Evaluate

$$\frac{2c\left(c-10d\right)}{5\left(c-2d\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{abc^{2}-10abcd}{3b^{2}c^{2}-6b^{2}cd}.

$$\frac{abc\left(c-10d\right)}{3c\left(c-2d\right)b^{2}}\times \frac{12bc^{2}d}{10acd}$$

Cancel out bc in both numerator and denominator.

$$\frac{a\left(c-10d\right)}{3b\left(c-2d\right)}\times \frac{12bc^{2}d}{10acd}$$

Cancel out 2cd in both numerator and denominator.

$$\frac{a\left(c-10d\right)}{3b\left(c-2d\right)}\times \frac{6bc}{5a}$$

Multiply \frac{a\left(c-10d\right)}{3b\left(c-2d\right)} times \frac{6bc}{5a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a\left(c-10d\right)\times 6bc}{3b\left(c-2d\right)\times 5a}$$

Cancel out 3ab in both numerator and denominator.

$$\frac{2c\left(c-10d\right)}{5\left(c-2d\right)}$$

Use the distributive property to multiply 2c by c-10d.

$$\frac{2c^{2}-20dc}{5\left(c-2d\right)}$$

Use the distributive property to multiply 5 by c-2d.

$$\frac{2c^{2}-20dc}{5c-10d}$$

Expand

$$\frac{2\left(10cd-c^{2}\right)}{5\left(2d-c\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{abc^{2}-10abcd}{3b^{2}c^{2}-6b^{2}cd}.

$$\frac{abc\left(c-10d\right)}{3c\left(c-2d\right)b^{2}}\times \frac{12bc^{2}d}{10acd}$$

Cancel out bc in both numerator and denominator.

$$\frac{a\left(c-10d\right)}{3b\left(c-2d\right)}\times \frac{12bc^{2}d}{10acd}$$

Cancel out 2cd in both numerator and denominator.

$$\frac{a\left(c-10d\right)}{3b\left(c-2d\right)}\times \frac{6bc}{5a}$$

Multiply \frac{a\left(c-10d\right)}{3b\left(c-2d\right)} times \frac{6bc}{5a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a\left(c-10d\right)\times 6bc}{3b\left(c-2d\right)\times 5a}$$

Cancel out 3ab in both numerator and denominator.

$$\frac{2c\left(c-10d\right)}{5\left(c-2d\right)}$$

Use the distributive property to multiply 2c by c-10d.

$$\frac{2c^{2}-20dc}{5\left(c-2d\right)}$$

Use the distributive property to multiply 5 by c-2d.

$$\frac{2c^{2}-20dc}{5c-10d}$$