$\text{Đáp án + Giải thích các bước giải:}$
`a//(x-5)+3(x-5)=0`
`<=>(x-5)(1+3)=0`
`<=>(x-5).4=0`
`<=>x-5=0`
`<=>x=5`
$\text{Vậy}$ `S={5}`
`b//(2x-1)/(3)-(5x+2)/(7)=x+13`
`<=>(7(2x-1))/(21)-(3(5x+2))/(21)=(21(x+13))/(21)`
`=>7(2x-1)-3(5x+2)=21(x+13)`
`<=>14x-7-15x-6=21x+273`
`<=>14x-15x-21x=7+6+273`
`<=>-22x=286`
`<=>x=-13`
$\text{Vậy}$ `S={-13}`
`c//(x-1)/(x+2)-(x)/(x-2)=(7x-6)/(4-x^{2})` `(ĐKXĐ:x\ne±2)`
`<=>((x-1)(x-2))/((x+2)(x-2))-(x(x+2))/((x-2)(x+2))=-(7x-6)/((x-2)(x+2))`
`⇒(x-1)(x-2)-x(x+2)=-(7x-6)`
`<=>x^{2}-3x+2-x^{2}-2x+7x-6=0`
`<=>2x-4=0`
`<=>2x=4`
`<=>x=2`
$\text{Vậy}$ `S={2}`
`d//(x+1)/(2021)+(x+2)/(2020)+(x+3)/(2019)+(x+4)/(2018)=-4`
`<=>((x+1)/(2021)+1)+((x+2)/(2020)+1)+((x+3)/(2019)+1)+((x+4)/(2018)+1)=0`
`<=>((x+1)/(2021)+(2021)/(2021))+((x+2)/(2020)+(2020)/(2020))+((x+3)/(2019)+(2019)/(2019))+((x+4)/(2018)+(2018)/(2018))=0`
`<=>(x+1+2021)/(2021)+(x+2+2020)/(2020)+(x+3+2019)/(2019)+(x+4+2018)/(2018)=0`
`<=>(x+2022)/(2021)+(x+2022)/(2020)+(x+2022)/(2019)+(x+2020)/(2018)=0`
`<=>(x+2022)((1)/(2021)+(1)/(2020)+(1)/(2019)+(1)/(2018))=0`
`<=>x+2022=0` $\text{. Do}$ `(1)/(2021)+(1)/(2020)+(1)/(2019)+(1)/(2018)\ne0`
`<=>x=-2022`
$\text{Vậy}$ `S={-2022}`
