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| 1. |
Solve for x : 1/x+1 + 2/x+2 = 4/x+4 , x not equal 1,-2-4. |
| Answer» {tex}\\frac { 1 } { x + 1 } + \\frac { 2 } { x + 2 } = \\frac { 4 } { x + 4 }{/tex}or,\xa0{tex}\\frac { x + 2 + 2 ( x + 1 ) } { ( x + 1 ) ( x + 2 ) } = \\frac { 4 } { x + 4 }{/tex}or,{tex}\\frac { 3 x + 4 } { x ^ { 2 } + 3 x + 2 } = \\frac { 4 } { x + 4 }{/tex}or,{tex}( 3 x + 4 ) ( x + 4 ) = 4 \\left( x ^ { 2 } + 3 x + 2 \\right){/tex}or,{tex}3 x ^ { 2 } + 16 x + 16 = 4 x ^ { 2 } + 12 x + 8{/tex}or,{tex}x ^ { 2 } - 4 x - 8 = 0{/tex}or,\xa0{tex}x = \\frac { - b \\pm \\sqrt { b ^ { 2 } - 4 a c } } { 2 a }{/tex}or,\xa0{tex}x = \\frac { - ( - 4 ) \\pm \\sqrt { ( - 4 ) ^ { 2 } - 4 ( 1 ) ( - 8 ) } } { 2 \\times 1 }{/tex}or,\xa0{tex}x = \\frac { 4 \\pm \\sqrt { 16 + 32 } } { 2 }{/tex}or,{tex}x = \\frac { 4 \\pm \\sqrt { 48 } } { 2 } = \\frac { 4 \\pm 4 \\sqrt { 3 } } { 2 }{/tex}or,\xa0{tex}x = 2 \\pm 2 \\sqrt { 3 }{/tex}Hence,\xa0{tex}x = 2 + 2 \\sqrt { 3 } \\text { or } 2 - 2 \\sqrt { 3 }{/tex} | |