Question

z^2-8z+15/z^2-25 simplify by method of factirization​

Answer 1

Answer:

${\sf{{\dfrac{z - 3}{z + 5}} }}$

Step-by-step explanation:

Given : ${\sf{\ \ {\dfrac{z^2 - 8z + 15}{z^2 - 25}} }}$

Using Middle Term Factorisation in numerator.

$\Rightarrow{\sf{ {\dfrac{z^2 - 3z - 5z + 15}{z^2 - 25}}}}$

Taking common terms out.

$\Rightarrow{\sf{ {\dfrac{z(z - 3) - 5(z - 3)}{z^2 - 25}}}}$

$\Rightarrow{\sf{ {\dfrac{(z - 5)(z - 3)}{z^2 - 25}}}}$

We can write the denominator as :

$\Rightarrow{\sf{ {\dfrac{(z - 5)(z - 3)}{(z)^2 - (5)^2}}}}$

• ${\boxed{\sf{\red{Identity \ : \ a^2 - b^2 = (a - b)(a + b)}}}}$

${\sf{\red{Here, \ a = z, \ b = 5}}}$

$\Rightarrow{\sf{ {\dfrac{(z - 5)(z - 3)}{(z - 5)(z + 5)}}}}$

Cancelling the common terms from the numerator and denominator.

$\Rightarrow{\sf{ {\dfrac{{\cancel{(z - 5)}}(z - 3)}{{\cancel{(z - 5)}}(z + 5)}}}}$

$\Rightarrow{\sf{ {\dfrac{(z - 3)}{(z + 5)}}}}$

$\Rightarrow{\boxed{\sf{\green{ {\dfrac{z - 3}{z + 5}}}}}}$

Answer 2

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