How will you simplify this expression  (x+y)^2-z^2 / (x+z)^2-y^2 to get x+y-z / x-y+z ? Please explain step by step, and especially what to do with the denominator?
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Using difference of two squares procedure, this becomes How will you simplify this expression  (x+y)^2-z^2 / (x+z)^2-y^2 to get x+y-z / x-y+z ? Please explain step by step, and especially what to do with the denominator?

Solve this  using the differnce of two square procedure. Viz. a^2 - b^2 = (a + b)(a - b)

You have:  {(x+y)^2-z^2} / {(x+z)^2-y^2 }

Numerator:  {(x+y)^2-z^2}

Using difference of two squares procedure, we get {(x+y)^2-z^2}​ = {x + y + z}{x + y - z}

Denominator:  {(x+z)^2-y^2}

Using difference of two squares procedure, we get {(x+z)^2-y^2}​ = {x + z + y}{x + z - y} = {x + y + z}{x - y + z}

Now, dividing numerator by denomiator, we get,

{x + y + z}{x + y - z}​ / {x + y + z}{x - y + z}​ = {x + y - z}​ / {x - y + z}​

Answer: {x + y - z}​ / {x - y + z}​​

by Level 11 User (80.9k points)

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