Đáp án+Giải thích các bước giải:
`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`
