Solve Rational Equations

common denominator is 6x ^{2}Why? because 6x^{2} can befactored into 3x•2x so thereis a factor of 2x already in 6x^{2}."multiply through" by 6x ^{2}. Whatthat means is that every numeratoris multiplied by 6x^{2}. Solving Rational Equations Using the "Multiply Through" Method Notice that on the 1/2x term I wrote6x ^{2} 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 6x ^{2}•-6 = 3x -2 = x 3 3 2x•3x• •6x ^{2}common denominator is x ^{2}+2xWhy? because x^{2}+2x can befactored into x•(x+2) so thereis a factor of x already in x^{2}+2x.Also the denominator of 1 is 1."multiply through" by x ^{2}+2x. Whatthat means is that every numeratoris multiplied by x^{2}+2x. Solving Rational Equations Using the "Multiply Through" Method (x ^{2}+2x)•Notice that on the "1" term nothing cancels.On the (x-1)/x term I wrote x ^{2}+2x asx(x+2) to make it more clear as to whatcancels and what is left.What is left to solve after canceling is: x ^{2}+2x = 1 + (x-1)•(x+2) x^{2}+2x = 1 + x^{2} + x -2The x ^{2} term on each side cancels: So,2x = x - 1 and x = -1 1 (x ^{2}+2x)••x(x+2) common denominator is 6b ^{2}Why? because 6b^{2} can be factoredinto 6•b•b so there is a factor of 6b & b & b^{2} already in 6b^{2}."multiply through" by 6b ^{2}. Whatthat means is that every numeratoris multiplied by 6b^{2}. 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 4b ^{2}. 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 m ^{2}-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 = x ^{2} - 9x + 8 +2x +2xWhat multiplies to +10 & adds to -7 ? - 2 = x ^{2} - 7x + 8+2 + 20 = x ^{2} - 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 = x ^{2} - 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 |

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