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common denominator is 6x2Why? because 6x2 can befactored into 3x•2x so thereis a factor of 2x already in 6x2. "multiply through" by 6x2. Whatthat means is that every numeratoris multiplied by 6x2. Solving Rational Equations Using the "Multiply Through" Method Notice that on the 1/2x term I wrote6x2 as 3x•2x to make it more clearas to what cancels and what is left. What is left to solve after canceling is: 1 = 3x + 7 -7 -7 6x2• -6 = 3x -2 = x 3 3 2x•3x• •6x2 common denominator is x2+2xWhy? because x2+2x can befactored into x•(x+2) so thereis a factor of x already in x2+2x.Also the denominator of 1 is 1. "multiply through" by x2+2x. Whatthat means is that every numeratoris multiplied by x2+2x. Solving Rational Equations Using the "Multiply Through" Method (x2+2x)• Notice that on the "1" term nothing cancels.On the (x-1)/x term I wrote x2+2x asx(x+2) to make it more clear as to whatcancels and what is left. What is left to solve after canceling is: x2+2x = 1 + (x-1)•(x+2) x2+2x = 1 + x2 + x -2 The x2 term on each side cancels: So, 2x = x - 1 and x = -1 1 (x2+2x)• •x(x+2) common denominator is 6b2Why? because 6b2 can be factoredinto 6•b•b so there is a factor of 6b & b & b2 already in 6b2. "multiply through" by 6b2. Whatthat means is that every numeratoris multiplied by 6b2. Solving Rational Equations Using the "Multiply Through" Method Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). common denominator is 4b2. Solving Rational Equations Using the "Multiply Through" Method Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). common denominator is m2-m = m•(m-1). Solving Rational Equations Using the "Multiply Through" Method Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). remember that 1 should bewritten as 1 Solving Rational Equations Using the "Multiply Through" Method 1 Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). remember that 1 should bewritten as 1 Solving Rational Equations Using the "Multiply Through" Method 1 Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). what is the common denominator? Solving Rational Equations Using the "Multiply Through" Method Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). common denominator is(x-1)•(x+1) -2•(x+1) = (x-8)•(x-1) -2x - 2 = x2 - 9x + 8 +2x +2x What multiplies to +10 & adds to -7 ? - 2 = x2 - 7x + 8+2 + 2 0 = x2 - 7x + 10 Solving Rational Equations Using the "Multiply Through" Method (x-1)•(x+1)• Notice that we are left with aquadratic which we will have to FOIL Set each factor equal to zero and solve. 0 = x2 - 7x + 100 = (x - 5)•(x - 2) x - 5 = 0 and x - 2 = 0 + 5 +5 + 2 +2 x = 5 •(x-1)•(x+1) x = 2 what is the common denominator? After "Multiply Through" you should geta quadratic which you will need to factorand solve. Notice there are now two answer boxes. Solving Rational EquationsUsing the "Multiply Through" Method Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). List the smaller answer first. and what is the common denominator? After "Multiply Through" you should geta quadratic which you will need to factorand solve. Notice there are now two answer boxes. Solving Rational EquationsUsing the "Multiply Through" Method Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). List the smaller answer first. and what is the common denominator? After "Multiply Through" you should geta quadratic which you will need to factorand solve. Notice there are now two answer boxes. Solving Rational EquationsUsing the "Multiply Through" Method Answer: As a whole number (like 2 or -7) or as a fraction (like 1/2 or -2/5). List the smaller answer first. and |