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Đáp án:
`a)`
`\frac{4xy-9}{7x^{2}y}+\frac{3xy+9}{7x^{2}y}` `(đk: x\ne0;y\ne0)`
`=\frac{4xy-9+3xy+9}{7x^{2}y}`
`=\frac{7xy}{7x^{2}y}`
`=\frac{1}{x}`
`b)`
`\frac{x+4}{2-x}-\frac{5x-4}{2-x}` `(đk: x\ne2)`
`=\frac{x+4-(5x-4)}{2-x}`
`=\frac{x+4-5x+4}{2-x}`
`=\frac{8-4x}{2-x}`
`=\frac{4.(2-x)}{2-x}`
`=4`
`c)`
`\frac{x^{2}-1}{x^{2}-2x}:\frac{x-1}{x-2}` `(đk: x\ne2;x\ne1;x\ne0)`
`=\frac{(x^{2}-1^{2})}{x.(x-2)}.\frac{x-2}{x-1}`
`=\frac{(x-1).(x+1).(x-2)}{x.(x-2).(x-1)}`
`=\frac{x+1}{x}`
`d)`
`\frac{x+1}{2x+6}+\frac{2x+3}{x^{2}+3x}` `(đk: x\ne0;x\ne-3)`
`=\frac{x+1}{2.(x+3)}+\frac{2x+3}{x.(x+3)}`
`=\frac{x.(x+1)}{2x.(x+3)}+\frac{(2x+3).2}{2x.(x+3)}`
`=\frac{x^{2}+x+4x+6}{2x.(x+3)}`
`=\frac{x^{2}+5x+6}{2x.(x+3)}`
`=\frac{x^{2}+2x+3x+6}{2x.(x+3)}`
`=\frac{x.(x+2)+3.(x+2)}{2x.(x+3)}`
`=\frac{(x+2).(x+3)}{2x.(x+3)}`
`=\frac{x+2}{2x}`
`e)`
`\frac{3}{3x-2}-\frac{5}{3x+2}+\frac{18-9x}{4-9x^{2}}` `(đk: x\ne\pm\frac{2}{3})`
`=\frac{3.(3x+2)}{(3x-2).(3x+2)}-\frac{5.(3x-2)}{(3x-2).(3x+2)}-\frac{18-9x}{(3x-2).(3x+2)}`
`=\frac{9x+6-15x+10-18+9x}{(3x-2).(3x+2)}`
`=\frac{(18x-15x)+(16-18)}{(3x-2).(3x+2)}`
`=\frac{3x-2}{(3x-2).(3x+2)}`
`=\frac{1}{3x+2}`
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