First, subtract color(red)(z)z and color(blue)(aw)aw from each side of the equation to isolate the aa terms while keeping the equation balanced:
ax - color(blue)(aw) + z - color(red)(z) = aw - color(blue)(aw) - y - color(red)(z)ax−aw+z−z=aw−aw−y−z
ax - aw + 0 = 0 - y - zax−aw+0=0−y−z
ax - aw = -y - zax−aw=−y−z
Next, factor an aa from each term on the left side of the equation:
a(x - w) = -y - za(x−w)=−y−z
Now, divide each side of the equation by color(red)(x - w)x−w to solve for aa while keeping the equation balanced:
(a(x - w))/color(red)(x - w) = (-y - z)/color(red)(x - w)a(x−w)x−w=−y−zx−w
(acolor(red)(cancel(color(black)((x - w)))))/cancel(color(red)(x - w)) = (-y - z)/(x - w)
a = (-y - z)/(x - w)
We can then multiply the right side of the equation by a form of 1 to rewrite the expression as:
a = (-1)/-1 xx (-y - z)/(x - w)
a = (-1(-y - z))/(-1(x - w))
a = (y + z)/(-x + w)
a = (y + z)/(w - x)