你可以说 "For the sake of you and me, I will change my Engpsh." 或者 "For our benefit, I will work on improving my Engpsh."
"For the sake of" 这个短语的意思是为了某人或某事的利益而做某事，常常用来表示为了达到某种目的而做出牺牲或努力。
举个例子：
"I'm going to study extra hard for the sake of getting into a good college." (为了能进入好的大学，我要特别努力学习。)
"She gave up her weekends for the sake of her job." (为了工作，她放弃了周末。)
希望这对你有帮助！