`1)` `1/{x+2}+1/{(x+2)(4x+7)}`
`\qquad (x\ne -2; x\ne -7/4)`
`={4x+7}/{(x+2)(4x+7)}+1/{(x+2)(4x+7)}`
`={4x+7+1}/{(x+2)(4x+7)}`
`={4x+8}/{(x+2)(4x+7)}`
$\\$
`2)` `{2x^2-x}/{x-1}+{x+1}/{1-x}+{2-x^2}/{x-1}` `(x\ne 1)`
`={2x^2-x}/{x-1}-{x+1}/{x-1}+{2-x^2}/{x-1}`
`={2x^2-x-x-1+2-x^2}/{x-1}`
`={x^2-2x+1}/{x-1}={(x-1)^2}/{x-1}`
`=x-1`
$\\$
`3)` `{3x+5}/{x^2-5x}+{25-x}/{25-5x}` `(x\ne 0;x\ne 5)`
`={3x+5}/{x(x-5)}+{x-25}/{5(x-5)}`
`={5(3x+5)}/{5x(x-5)}+{x(x-25)}/{5x(x-5)}`
`={15x+25+x^2-25x}/{5x(x-5)}`
`={x^2-10x+25}/{5x(x-5)}`
`={(x-5)^2}/{5x(x-5)}`
`={x-5}/{5x}`
$\\$
`4)` `5/{2x^2y}+3/{5xy^2}+x/{y^3}` `(x\ne 0;y\ne 0)`
`={5.5.y^2}/{10x^2y^3}+{3.2.xy}/{10x^2y^3}+{x.10x^2}/{10x^2y^3}`
`={25y^2+6xy+10x^3}/{10x^2y^3}`