Question

(x+10)/4x+10 = (x+6)/(x+10)​

Answer 1

We are given :-

• $\sf\:\dfrac{(\:x\:+\:10\:)}{(\:4x\:+\:10\:)}\:=\:\dfrac{(\:x\:+\:6\:)}{(\:x\:+\:10\:)}$

According to the given question, we are asked to find the value of x.Here's our required solution!

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$\sf \red{{\:\dfrac{(\:x\:+\:10\:)}{(\:4x\:+\:10\:)}\:=\:\dfrac{(\:x\:+\:6\:)}{(\:x\:+\:10\:)}}}\\\\\\:\implies\sf\:(\:x\:+\:10\:)\:\times\:(\:x\:+\:10\:)\:=\:(\:x\:+\:6\:)\:\times\:(\:4x\:+\:10\:)\\\\\\:\implies\sf\:(\:x\:+\:10\:)^2\:=\:4x^2\:+\:10x\:+\:24x\:+\:60\\\\\\:\implies\sf\:x^2\:+\:2\:\times\:x\:\times\:10\:+\:(\:10\:)^2\:=\:4x^2\:+\:34x\:+\:60\\\\\\:\implies\sf\:x^2\:+\:20x\:+\:100\:=\:4x^2\:+\:34x\:+\:60\\\\\\:\implies\sf\:4x^2\:+\:34x\:+\:60\:-\:x^2\:-\:20x\:-\:100\:=\:0\\\\\\:\implies\sf\:4x^2\:-\:x^2\:+\:34x\:-\:20x\:-\:100\:+\:60\:=\:0\\\\\\:\implies\sf\:3x^2\:+\:14x\:-\:40\:=\:0\\\\\\:\implies\sf\:3x^2\:+\:20x\:-\:6x\:-\:40\:=\:0\\\\\\:\implies\sf\:3x^2\:-\:6x\:+\:20x\:-\:40\:=\:0\\\\\\:\implies\sf\:3x\:(\:x\:-\:2\:)\:+\:20\:(\:x\:-\:2\:)\:=\:0\\\\\\:\implies\sf\:(\:x\:-\:2\:)\:(\:3x\:+\:20\:)\:=\:0\\\\\\:\implies\sf\:x\:-\:2\:=\:0\:\:\:or\:\:\:3x\:+\:20\:=\:0\\\\\\:\implies\sf\:x\:=\:2\:\:\:or\:\:\:3x\:=\:-\:20\\\\\\:\implies\boxed{\red{\sf\:x\:=\:2}}\sf\:\:\:or\:\:\:\boxed{\red{\sf\:x\:=\:-\:\dfrac{20}{3}}}$

Answer 2

Step-by-step explanation:

x+10/4x+10 = x+6/x+10

x+10(x+10) = x+6 (4x+10)

${x}^{2} + 10x + 10x + 100 = 4 {x}^{2} + 10x + 24x + 60$

${x}^{2} - 4 {x }^{2} + 10x - 34x + 100 - 60 = 0$

$- 3 {x }^{2} - 14x + 40 = 0$

Hence, the required equation