class fraction {
  n;
  d;
  s;

  constructor(n, d) {
    const g = this.gcd(Math.abs(n), Math.abs(d));
    this.n = Math.abs(n / g);
    this.d = Math.abs(d / g);
    this.s = n * d < 0 ? -1 : 1;
  }

add(f) {
    const n = this.s * this.n * f.d + f.s * f.n * this.d;
    const d = this.d * f.d;
    return new fraction(n, d);
  }

  sub(f) {
    const n = this.s * this.n * f.d - f.s * f.n * this.d;
    const d = this.d * f.d;
    return new fraction(n, d);
  }

  mul(f) {
    const n = this.s * this.n * f.s * f.n;
    const d = this.d * f.d;
    return new fraction(n, d);
  }

  div(f) {
    const n = this.s * this.n * f.d;
    const d = this.d * f.s * f.n;
    return new fraction(n, d);
  }

  gcd(a, b) {
    return b === 0 ? a : this.gcd(b, a % b);
  }
}

export function frac(f, mid=false) {
  const pos = mid ? "+" : "";
  const sgn = f.s == -1 ? "-" : pos;
  if (f.d == 1) return `${sgn}${f.n}`;
  return `${sgn}\\frac{${f.n}}{${f.d}}`;
}

function gcd(a ,b){
    if(b == 0) return a;
    return gcd(b, a % b);
}

function equation(ptA, ptB){
    const [xA, yA] = ptA;
    const [xB, yB] = ptB;
    let dx = xB - xA;
    let dy = yB - yA;
    if(dx == 0) return `x=${xA}`; 
    if(dy == 0) return `y=${yA}`;
    const a = new fraction(dy, dx);
    const b = new fraction(dx * yA - dy * xA, dx)
    return `${frac(a)}x${b.n === 0 ? "" : frac(b, true)}`;    
}

console.log(equation([2, 2], [0, 0]))