Rút gọn `A` `A= ( (x-2)/(2x-2) + 3/(2x-2) - (x+3)/(2x+2) ) : ( 1 - (x-3)/(x+1) )`
2 câu trả lời
` A = ( [ x - 2 ] / [ 2x - 2 ] + 3 / [ 2x - 2 ] - [ x + 3 ] / [ 2x + 2 ] ) : ( 1 - [ x - 3 ] / [ x + 1 ] ) `
` A = ( [ x - 2 + 3 ] / [ 2x - 2 ] - [ x + 3 ] / [ 2x + 2 ] ) : ( [ x + 1 ] / [ x + 1 ] - [ x - 3 ] / [ x + 1 ] ) `
` A = ( [ x + 1 ] / [ 2 ( x - 1 ) ] - [ x + 3 ] / [ 2 ( x + 1 ) ] ) : [ x + 1 - x + 3 ] / [ x + 1 ] `
` A = [ ( x + 1 ) ( x + 1 ) - ( x + 3 ) ( x - 1 ) ] / [ 2 ( x - 1 ) ( x + 1 ) ] : 4 / [ x + 1 ] `
` A = [ x² + 2x + 1 - ( x² + 2x - 3 ) ] / [ 2 ( x - 1 ) ( x + 1 ) ] . [ x + 1 ] / 4 `
` A = [ x² + 2x + 1 - x² - 2x + 3 ] / [ 2 ( x - 1 ) ] . 1/4 `
` A = 4 / [ 2 ( x - 1 ) ] . 1/4 `
` A = 1 / [ 2 ( x - 1 ) ] `
Vậy ` A = 1 / [ 2 ( x - 1 ) ] `
`A=( (x-2)/(2x-2) + 3/(2x-2) - (x+3)/(2x+2)) : (1- (x-3)/(x+1))`
`= [(x+1)/(2(x-1)) - (x+3)/(2(x+1))] : 4/(x+1)`
`= [ ((x+1)^2)/(2(x-1)(x+1)) - ((x+3)(x-1))/(2(x+1)(x-1))] : 4/(x+1)`
`= (x^2+2x+1 - x^2 - 2x + 3)/(2(x^2-1)) . (x+1)/4`
`= 4/(2(x-1)(x+1)) . (x+1)/4`
`= 1/(2(x-1)`
Vậy `A = 1/(2(x-1)`