Adding and Subtracting

Algebra 1 · Axiom Academy

LESSON Adding & Subtracting Rational Expressions Find a common denominator by factoring, scale each fraction up to it, then combine the numerators — exactly like adding ordinary fractions. You can only add fractions when the pieces are the same size. The denominator sets the size of each piece, so before adding we rewrite both fractions over one shared denominator. Watch the warm-up : the two unequal pieces both rescale to twelfths, and only then do the numerators add. With polynomials you can't eyeball the LCD — you have to factor first. Factoring breaks each denominator into irreducible pieces; the LCD is then the union of those pieces, each taken to the highest power it reaches in any denominator. Watch x^2-4 and x^2-4x+4 split into factors, then the distinct factors collect into one bin to form the LCD. 3. Adding: Scale Up, Then Combine Now the full operation. Add . The LCD is the union of factors: x(x+3)(x-2) . Each fraction is missing exactly one factor of the LCD, so multiply top and bottom by that missing piece, then add the numerators. Watch each fraction get scaled up to the LCD by its missing factor, then the two numerators merge into one. The numerator 7x-4 shares no factor with the denominator, so the answer is already in lowest terms. 4. Subtracting with a Repeated Factor Subtraction adds one trap: the minus sign distributes across the entire second numerator. Compute . The factor (x-1) appears squared, so the LCD is (x-1)^2(x+2) .

This is the written version of the interactive lesson above. See the full Algebra 1 course.