Verified answer

Answer:

[tex]3x - 13 = \frac{30}{x} [/tex]

[tex]x(3x - 13) = 30[/tex]

[tex] 3{x}^{2} - 13x - 30 = 0[/tex]

[tex]3 {x}^{2} - (18 - 5)x - 30 = 0[/tex]

[tex]3 {x}^{2} - 18x + 5 x- 30 = 0[/tex]

[tex]3x(x - 6) + 5(x - 6) = 0[/tex]

[tex](3x + 5)(x - 6) = 0[/tex]

[tex]either [/tex]

[tex](3x + 5) = 0[/tex]

[tex]3x = - 5[/tex]

[tex]x = \frac{ - 5}{3} [/tex]

[tex]or[/tex]

[tex](x - 6 )= 0[/tex]

[tex] x= 6[/tex]

therefore, the factors of the given equation are -5/3 and 6.