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Question Number 97496 by shaxzod last updated on 08/Jun/20

$$iff\left(\frac{2x+5}{x-3}\right)=3x+5findf\left(x\right)$$$$$$$$pleasesolveit$$

Answered by bobhans last updated on 08/Jun/20

$$\mathrm{set}\frac{2\mathrm{x}+5}{\mathrm{x}-3}=\mathrm{z}\Rightarrow \mathrm{xz}-3\mathrm{z}=2\mathrm{x}+5$$$$\mathrm{xz}-2\mathrm{x}=5+3\mathrm{z}\Rightarrow \mathrm{x}=\frac{5+3\mathrm{z}}{\mathrm{z}-2}$$$$\mathrm{f}\left(\mathrm{z}\right)=3\left(\frac{5+3\mathrm{z}}{\mathrm{z}-2}\right)+5\Rightarrow \mathrm{f}\left(\mathrm{x}\right)=\frac{15+9\mathrm{x}}{\mathrm{x}-2}+5$$$$\frac{15+9\mathrm{x}+5\mathrm{x}-10}{\mathrm{x}-2}=\frac{14\mathrm{x}+5}{\mathrm{x}-2}$$

Commented by shaxzod last updated on 08/Jun/20

$$thankyou$$

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