![\dfrac{\frac{x+2}{x^2+2x-3}}{\frac{x+2}{x^2-x}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7Bx%2B2%7D%7Bx%5E2%2B2x-3%7D%7D%7B%5Cfrac%7Bx%2B2%7D%7Bx%5E2-x%7D%7D)
If
, then we can immediately cancel the factors of
:
![\dfrac{\frac1{x^2+2x-3}}{\frac1{x^2-x}}=\dfrac{x^2-x}{x^2+2x-3}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac1%7Bx%5E2%2B2x-3%7D%7D%7B%5Cfrac1%7Bx%5E2-x%7D%7D%3D%5Cdfrac%7Bx%5E2-x%7D%7Bx%5E2%2B2x-3%7D)
Factorize the numerator and denominator:
![x^2-x=x(x-1)](https://tex.z-dn.net/?f=x%5E2-x%3Dx%28x-1%29)
![x^2+2x-3=(x+3)(x-1)](https://tex.z-dn.net/?f=x%5E2%2B2x-3%3D%28x%2B3%29%28x-1%29)
Next, if
, then
![\dfrac{x^2-x}{x^2+2x-3}=\dfrac{x(x-1)}{(x+3)(x-1)}=\dfrac x{x+3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2-x%7D%7Bx%5E2%2B2x-3%7D%3D%5Cdfrac%7Bx%28x-1%29%7D%7B%28x%2B3%29%28x-1%29%7D%3D%5Cdfrac%20x%7Bx%2B3%7D)
$47.88 your answer and I am the most important person in the world.
Step-by-step explanation:
![\sf{\bold{\blue{\underline{\underline{Given}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cblue%7B%5Cunderline%7B%5Cunderline%7BGiven%7D%7D%7D%7D%7D)
![\tt{\angle{c}=110°}](https://tex.z-dn.net/?f=%5Ctt%7B%5Cangle%7Bc%7D%3D110%C2%B0%7D)
and,
![\tt{BC=AC}](https://tex.z-dn.net/?f=%5Ctt%7BBC%3DAC%7D%20%20)
⠀⠀⠀⠀
![\sf{\bold{\red{\underline{\underline{To\:Find}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cred%7B%5Cunderline%7B%5Cunderline%7BTo%5C%3AFind%7D%7D%7D%7D%7D)
☆Find the ![\angle{B} ~and~\angle{A}](https://tex.z-dn.net/?f=%5Cangle%7BB%7D%20~and~%5Cangle%7BA%7D%20%20)
![\sf{\bold{\purple{\underline{\underline{Solution}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cpurple%7B%5Cunderline%7B%5Cunderline%7BSolution%7D%7D%7D%7D%7D)
Here,
BC =AC
so,
⠀⠀⠀
![\angle{A}=\angle{B}](https://tex.z-dn.net/?f=%5Cangle%7BA%7D%3D%5Cangle%7BB%7D%20%20)
we know that,
![\tt{\boxed{\pink{\angle{A}+\angle{B}+\angle{C}=180°}}}](https://tex.z-dn.net/?f=%5Ctt%7B%5Cboxed%7B%5Cpink%7B%5Cangle%7BA%7D%2B%5Cangle%7BB%7D%2B%5Cangle%7BC%7D%3D180%C2%B0%7D%7D%7D%20%20)
But
(Ģìvéñ)
so..
![\angle{A}+\angle{B}+110°=180°](https://tex.z-dn.net/?f=%5Cangle%7BA%7D%2B%5Cangle%7BB%7D%2B110%C2%B0%3D180%C2%B0%20%20)
![\angle{A}+\angle{A}+110°=180°](https://tex.z-dn.net/?f=%5Cangle%7BA%7D%2B%5Cangle%7BA%7D%2B110%C2%B0%3D180%C2%B0%20%20)
![\because{\angle{A}=\angle{B} }](https://tex.z-dn.net/?f=%5Cbecause%7B%5Cangle%7BA%7D%3D%5Cangle%7BB%7D%20%7D%20%20)
![2\angle{A}=180°-110°](https://tex.z-dn.net/?f=2%5Cangle%7BA%7D%3D180%C2%B0-110%C2%B0%20%20)
![2\angle{A}=70°](https://tex.z-dn.net/?f=2%5Cangle%7BA%7D%3D70%C2%B0%20%20)
![\angle{A}=\dfrac{70°}{2}](https://tex.z-dn.net/?f=%5Cangle%7BA%7D%3D%5Cdfrac%7B70%C2%B0%7D%7B2%7D%20%20)
![\boxed{\orange{\angle{A}=35°}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Corange%7B%5Cangle%7BA%7D%3D35%C2%B0%7D%7D%20%20)
But...
![\angle{A}=\angle{B}](https://tex.z-dn.net/?f=%5Cangle%7BA%7D%3D%5Cangle%7BB%7D%20%20)
soo,
![\boxed{\orange{\angle{B}=35°}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Corange%7B%5Cangle%7BB%7D%3D35%C2%B0%7D%7D%20%20)
![\sf{\bold{\green{\underline{\underline{Answer}}}}}](https://tex.z-dn.net/?f=%5Csf%7B%5Cbold%7B%5Cgreen%7B%5Cunderline%7B%5Cunderline%7BAnswer%7D%7D%7D%7D%7D)
⠀⠀⠀⠀
![\boxed{\green{\angle{A}=35°}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cgreen%7B%5Cangle%7BA%7D%3D35%C2%B0%7D%7D%20%20)
![\boxed{\green{\angle{B}=35°}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cgreen%7B%5Cangle%7BB%7D%3D35%C2%B0%7D%7D%20%20)
The value of y=29
the value of x=61