Solve 343n-175/7n^2-19n+10div35n^2+4n-15/n^2-7n+10

$$\frac { 343 n - 175 } { 7 n ^ { 2 } - 19 n + 10 } \div \frac { 35 n ^ { 2 } + 4 n - 15 } { n ^ { 2 } - 7 n + 10 }$$

Evaluate

$$\frac{7\left(n-5\right)\left(49n-25\right)}{\left(5n-3\right)\left(49n^{2}-25\right)}$$

Short Solution Steps

Divide \frac{343n-175}{7n^{2}-19n+10} by \frac{35n^{2}+4n-15}{n^{2}-7n+10} by multiplying \frac{343n-175}{7n^{2}-19n+10} by the reciprocal of \frac{35n^{2}+4n-15}{n^{2}-7n+10}.

$$\frac{\left(343n-175\right)\left(n^{2}-7n+10\right)}{\left(7n^{2}-19n+10\right)\left(35n^{2}+4n-15\right)}$$

Factor the expressions that are not already factored.

$$\frac{7\left(n-5\right)\left(n-2\right)\left(49n-25\right)}{\left(n-2\right)\left(5n-3\right)\left(7n-5\right)\left(7n+5\right)}$$

Cancel out n-2 in both numerator and denominator.

$$\frac{7\left(n-5\right)\left(49n-25\right)}{\left(5n-3\right)\left(7n-5\right)\left(7n+5\right)}$$

Expand the expression.

$$\frac{343n^{2}-1890n+875}{245n^{3}-147n^{2}-125n+75}$$

Expand

$$\frac{7\left(49n^{2}-270n+125\right)}{\left(7n-5\right)\left(35n^{2}+4n-15\right)}$$

Short Solution Steps

Divide \frac{343n-175}{7n^{2}-19n+10} by \frac{35n^{2}+4n-15}{n^{2}-7n+10} by multiplying \frac{343n-175}{7n^{2}-19n+10} by the reciprocal of \frac{35n^{2}+4n-15}{n^{2}-7n+10}.

$$\frac{\left(343n-175\right)\left(n^{2}-7n+10\right)}{\left(7n^{2}-19n+10\right)\left(35n^{2}+4n-15\right)}$$

Factor the expressions that are not already factored.

$$\frac{7\left(n-5\right)\left(n-2\right)\left(49n-25\right)}{\left(n-2\right)\left(5n-3\right)\left(7n-5\right)\left(7n+5\right)}$$

Cancel out n-2 in both numerator and denominator.

$$\frac{7\left(n-5\right)\left(49n-25\right)}{\left(5n-3\right)\left(7n-5\right)\left(7n+5\right)}$$

Expand the expression.

$$\frac{343n^{2}-1890n+875}{245n^{3}-147n^{2}-125n+75}$$