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Fractional Equations Solving Fractional Equations Unknown Variables in More Than One Term Common Electronics Equations Roots of Quadratic Equations Quadratic Formula Solving Fractional Equations Rule 9-1: To solve an equation that includes fractions or mixed numbers: 1. get rid of the fraction (or mixed number); 2. solve for the unknown; 3. verify your answer. 1/3 + a/4 = 2 12(1/3 + a/4) = 2•12 4 + 3a = 24 3a = 20 a = 20/3 = 6 2/3 Unknown Variables in More Than One Term Key Point: When unknown variables appear in more than one term, we must factor out the unknown to arrive at a solution. ER, = V1R1 + V2R2 Solve for R1 . ER1 - VIR1 = V2R2 R1(E - V1) = V2R2 R1 = V2R2 / (E - V1) Common Electronics Equations The value of total resistance of two resistors in parallel. RT R1 R 2 R1R 2 The voltage gain of a non-inverting op-amp amplifier. AV Rf 1 Rin Roots of Quadratic Equations Key Point: Quadratic equations are second-degree equations and have two solutions or roots x2 + 7x + 12 = 0 (x + 3)(x + 4) = 0 x + 3 = 0 x = -3 x + 4 = 0 x = -4 Quadratic Formula b b 4ac 2a 2 You can apply the quadratic formula to a quadratic equation in the form ax2 + bx + c = 0