Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$$\frac{4x^2-13xt+9t^2}{3x^2t^2}$$
In order to add or subtract fractions, we must first make sure that the denominators are the same. After we create like denominators, we combine the numerators together to get the new fraction. Doing this, we find: $$\frac{\left(4x+2t\right)x}{3x^2t^2}-\frac{\left(5x-3t\right)\cdot \:3t}{3x^2t^2}\\ \frac{\left(4x+2t\right)x-\left(5x-3t\right)\cdot \:3t}{3x^2t^2}\\ \frac{4x^2-13xt+9t^2}{3x^2t^2}$$