Question

How do you do this problem?

Answer 1

Step One

Put the right side over a common denominator.

$\dfrac{a(x+ 1)}{*(x + 1)} - \dfrac{bx}{x(x + 1)} = \dfrac{ax+a - bx}{x(x + 1)} = \dfrac{ax - bx + a}{x(x + 1)}$

Step Two

Remove the brackets on the numerator in the last equality.

Step three.

This will seem kind of odd but take out the common factor (x) in the first two terms of the numerator.

$\dfrac{x(a - b) + a}{x(x + 1)}$

Step Four

What you do next comes up very frequently in your second or third calculus course.

You have to notice that there are no xs in the numerators on the left side of the original expression

Therefore you have to make a - b = 0 so that the xs disappear on the right.

a - b =0

a = b

Step Five

Find a

a is all by itself on the numerator of the final result.

The original question has a 1 in the numerator. Therefore a = 1

Step Six

Solve for b

a = b

1 = b Answer