Đáp án+Giải thích các bước giải:
`a)A=(x/(x+2)+1) : (1- (3x^2)/(4-x^2))` `(ĐKXĐ: x\ne±2;x\ne ±1)`
`=(x+x+2)/(x+2) : (4-x^2-3x^2)/(4-x^2)`
`=(2x+2)/(x+2) : (4-4x^2)/(4-x^2)`
`=(2x+2)/(x+2) : [(2-2x)(2+2x)]/[(2-x)(2+x)]`
`=(2x+2)/(x+2) * [(2-x)(2+x)]/[(2-2x)(2+2x)]`
`= (2-x)/(2-2x)`
`b)B=((2a^2)/(b^2)-1/2) . (1/(2a-b)-1/(2a+b))` `(ĐKXĐ: a\ne ± 2b;a\ne0)`
`=((4a^2)/(2b^2)-(b^2)/(2b^2)) . (2a+b-(2a-b))/[(2a-b)(2a+b)]`
`=(4a^2-b^2)/(2b^2) * (2a+b-2a-b)/[(2a-b)(2a+b)]`
`=(4a^2-b^2)/(2b^2) * (2b)/(4a^2-b^2)`
`=1/b`
`c)C=(3/(x+3)-3/(x^2+6x+9)) : (3/(x^2-9)+1/(3-x))` `(ĐKXĐ: x\ne ± 3;x\ne0)`
`=(3/(x+3)-3/(x+3)^2) : (3/[(x-3)(x+3)]-1/(x-3))`
`=[3(x+3)-3]/(x+3)^2 : [3-(x+3)]/[(x+3)(x-3)]`
`=(3x+9-3)/(x+3)^2 : (3-x-3)/[(x+3)(x-3)]`
`=(3x+6)/(x+3)^2 : (-x)/[(x-3)(x+3)]`
`=(3x+6)/(x+3)^2 * [(x-3)(x+3)]/(-x)`
`=[(3x+6)(x-3)]/[(-x)(x+3)]`
`=(3x^2-9x+6x-18)/(-x^2-3x)`
`=(3x^2-3x-18)/(-x^2-3x)`
`=(18+3x-3x^2)/(x^2+3x)`
`d)D=((4a+b)/(a^2-4ab)+(4a-b)/(a^2+4ab)). (a^2-16b^2)/(a^2+b^2)` `ĐKXĐ: a\ne ±4b;a\ne0)`
`=((4a+b)/[a(a-4b)]+(4a-b)/[a(a+4b)]) (a^2-16b^2)/(a^2+b^2)`
`=((4a+b)(a+4b)+(4a-b)(a-4b))/[a(a-4b)(a+4b)] * [(a-4b)(a+4b)]/(a^2+b^2)`
`=(4a^2+16ab+ab+4b^2+4a^2-16ab-ab+4b^2)/a * 1/(a^2+b^2)`
`=(8a^2+8b^2)/a * 1/(a^2+b^2)`
`=[8(a^2+b^2)]/a *1/(a^2+b^2)`
`=8/a`
