Выполните действия: [latex] frac{x+4}{x-1} - frac{37x-12}{4x^2-3x-1} [/latex]

[latex]frac{x+4}{x-1}-frac{37x-12}{4x^2-3x-1}=frac{x+4}{x-1}-frac{37x-12}{(4x+1)(x-1)}=frac{(x+4)(4x+1)-(37x-12)}{(4x+1)(x-1)}=\=frac{4x^2+17x+4-37x+12}{(4x+1)(x-1)}=frac{4x^2-20x+20}{(4x+1)(x-1)}[/latex]

[latex] frac{x+4}{x-1} - frac{37x-12}{4x^2-3x-1} = frac{x+4}{x-1} - frac{37x-12}{4x^2-4x+x-1}= frac{x+4}{x-1} - frac{37x-12}{(x-1)(4x+1)}= \ = frac{(x+4)(4x+1)-37x+12}{(x-1)(4x+1)} = frac{4x^2+x+16x+4-37x+12}{(x-1)(4x+1)} = frac{4x^2-20x+16}{(x-1)(4x+1)} =\ = frac{4(x^2-5x+4)}{(x-1)(4x+1)} = frac{4(x^2-x-4x+4)}{(x-1)(4x+1)} = frac{4(x-4)(x-1)}{(x-1)(4x+1)} =frac{4(x-4)}{4x+1} =frac{4x-16}{4x+1} [/latex]