3. Solve for   x   and check

This is a rational equation, so we need to clear denominators. Multiply both sides by   cx + d.

ax + b = cx + d

There are no parentheses to remove or like terms to combine so we transpose   x   terms to one side and terms that do not have a factor of   x   to the other side.

ax - cx = d - b

Since we have moved all the terms that have   x's   to the left, and gotten rid of all terms on the left that don't, we will be able to factor out an   x   from all the terms on the left.

(a - c)x = d - b

This gets all of the   x's   together in one place where only one thing is happening to it. It is being multiplied by   (a - c)  , so to get rid of it, divide both sides by   (a - c).

Check.

Copy down the original equation,

except that wherever you see an   x,   copy down the solution.

We have an addition of fractions problem on both the top and bottom. For this we will need common denominators.

Now that we have common denominators for the top and bottom, remove parentheses in the tops.

We see that some of the terms on the tops will cancel out.

and we don't even need to invert and multiply so see that the expression simplifies to

= 1

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